Why should I not use my religion (though it's much more accurately described as faith) as the sole reason for my deciding something? After all, there are plenty of people who use their lack of religion/faith as the sole reason to believe a certain way? I mean, if I believe that the Bible is the word of God, and God says X, then why should I not believe X based solely on that reason? It doesn't seem much different than believing we've visited the moon, since all we have is the word of NASA, and there are a lot of people who think we never did.
If you can say that you have acted in compliance with the overall terms of your faith in the way that you voted, you may not have done anything wrong, if your kindness, reservation of judgment, life by example instead of force, and care of your fellow man are the primary tenets of your faith.
But, even then, you having done the right thing would not be because you did so purely on religious teachings, but because both your vote and your choice of faith were derived from your innate understanding of the importance of justice, civil rights, kindness, love, acceptance and humility.
So, some of your question has to do with how much your decision is because of your faith and attempt to emulate your deity, versus religious teachings within your personal sect.
Your religion should not be your only reason to vote, because that says that you are not capable of faith if you are not capable of thought about issues and how they reflect upon God instead of the literal following of rules. As an example, from the Bible, the Pharisees brought a folded over crippled woman to Jesus to heal on the Sabbath to prove that he would break the laws of his religious teachings. Jesus' answer was that the laws existed for us as a tool to help people and ourselves, but that it did not replace thought about our actions and behaving in the way most consistent with God's most important priorities, even if that meant the breaking of God's law. To say that your religion is your sole reason, is to say that you did not think about your decision in enough detail for it to reflect your faith. Faith is a choice based on many things including feelings and teachings and personal morals and ethics. It is a call to you to use your best judgment in analyzing all of the reasons to vote for or against something. In analyzing all of the reasons to vote for or against something, it can no longer be said that you are voting _solely_ on the basis of your faith, but rather your choice of behaviors and options most consistent with the intent of the deity in whom you place your faith.
To put it the way you put it above is to put the cart before the horse. Faith was never meant as a replacement for thought. It was never meant as a set of unbreakable laws. It was meant as a choice to take care and try to understand all things and make your choices carefully and with love. If you are no longer making choices carefully with love, but only following rules or seeing black and white, you have fallen into dogma, rather than faith, because faith cannot truly exist unless questioned moment to moment throughout your life within the reference of every decision you make. Your language reflects a lack of respect for the teachings of your own deity if you meant them that way, and a dangerous sloppiness, if not meant that way.
If your religion is based on the Bible, voting for legislation which prevents or removes rights or privileges from people whose behavior you do not agree with or have decided based on your own interpretation of God's word, that he doesn't agree with, is committing crimes against your fellow man in judging them in Jesus' and God's stead, which he has specifically counseled against in the Bible as only his right to do. Legislation meant to _prevent_ liberty or _force_ compliance with your rules with the only justification being in terms of faith or religion, is a statement that you have abdicated your responsibility to these individual people as a Christian, and you presume to know more than any deities available to us as to his/their plan for each person created, so that you might choose between them and inflict your faith and rules derived thereof on other people God had other plans for without having to do the work to behave in a Christian way.
I think that you would not feel nearly so comfortable about faith being intrinsically inter-related with government as the only deciding factor if we were to import 50 million Muslims to this country from the Middle East, and have all of them pass legislation against you that you should wear a burka and practice Muslim religion or be stoned to death in the streets. They believe as strongly as you do in your religion’s correctness, and many of them are equally willing to abandon thought in exchange for dogmatic rules.
To make political decisions for singular causes is to prove that you should not be trusted as a thinking, educated person and therefore, should not be given the right to vote. Saying that you make political decisions based on careful understanding of as much information as is available to you, and which is consistent with your faith, is a very different thing.
So the answer to your question as to why you shouldn't vote just because of your faith while some vote just because they don't have faith, is the above, as well as partially that you are failing to understand the accurate comparison for your behavior within the context of your own religious structure, and in so doing, damming yourself as a false prophet before God. According to the Bible and most of the other religious texts I have read, you are not supposed to select your behavior based on the behavior of men (who vote just because they don't have faith), but rather based on the thoughtful consideration of instruction of your deity of choice and whether the rules of your faith are appropriate to this situation.
Another part of the answer is that certain voting decisions reflect a failing of your faith, because faith includes acting in a kind and Christian way in the face of behavior your disagree with, not in attempting to legislatively suppress behavior you have decided you have the authority to declare that God doesn't like and should be prevented. Because you consider someone else’s behavior to be dangerous to your faith if not suppressed, you must not truly have faith, because faith means trust in the divinity of God and his power to cause that which he desires from his people through the kind and loving Christian acts of his people.
For example, prison is a failure of faith within Christianity. It is a convenience based on laziness and in some people, fear. God would have you take those people into your home and show them a Christian way of life and reform their choices and behavior through charity, trusting that God would provide for you and protect you as is consistent with his plan for your life. The same is true of legislation designed to remove or prevent rights from people. That is a convenience out of laziness that is in direct contradiction with the religious teachings of kindness and love and life by example and pulling those people who are struggling into your church family rather than passing them off to the law to handle for you. It is a short cut to appease guilt that fails to meet God's requirements for your behavior.
Legislating your faith is a clear statement to many of us that you are a Pharisee who does not in truth have faith, because true faith could not be threatened by the behavior of anyone else on this plane of existence.
Because we, even when not Christian, are often capable of more Christian behavior than many Christians, we tend to try to assume the best of everyone. This manifests in a belief that you are too scared to follow your true faith and calling. Our alternatives are to consider you too stupid to understand the veritable cornucopia of passages in the Bible that talk of kindness, reserving judgment, infinite hope, and action through loving behavior, charity, personal sacrifice, etc, or we could assume that you know full well that you are defying your own savior's teachings and simply do not care because you have justified your behavior out of false righteousness, or we could decide that you are simply using your pretense of a faith that doesn’t really exist as a tool of suppression and hatred toward your fellow man intentionally.
As a person who considers herself to have faith, I would personally rather be thought scared and ignorant than dim and self righteous and cruel, myself. But then, I already understand that legislation is destined to failure that will not in any way serve in my stead for hard work of bringing my beliefs to people individually and showing them why those beliefs are something they should participate in, whether those beliefs relate to sexual preference, abortion or anything else that I have issues with. I understand that I cannot expect a political system to prevent my need for personal hard work, nor am I naive enough to believe that a political system can even prevent behavior I disagree with rather than punish it retrospectively, which is not consistent with my understanding of God. It is not the government’s job to teach people what is right. It is their job only to manage those with whom I fail in as fair and non-biased, non-partisan way as possible.
I'll ask as bluntly as I know how, since trying to be "polite" about it tends to blur my point: Do you, a gay person, see a difference between my love for you, the person, and my refusal to accept as moral your homosexual behaviour? Do you believe this is possible or is it just a cop-out?
Yes, I can see a difference between your love for me, the person, and my behaviors. I have a great deal of respect for your capacity to differentiate between those two things. I can also see the difference between your professed beliefs and your behaviors in your handling of your unwillingness to accept my behavior, and your failure to earn my respect by understanding that differentiation. As for your acceptance of behavior you believe God disapproves of, you are not being asked to participate in that behavior in any way personally, either to have gay sex or marry two gay people and therefore, until you are, you do not have the opportunity or right to truthfully accept or reject that behavior so long as it is between consenting adults. What you are doing in actuality, is judging and attempting to suppress that behavior, which is something that makes you just as much a sinner and failure as a Christian as I may be because of my sexual orientations. When I find myself in such situations, I attempt to avoid throwing stones as I believe that is what God would have of me.
We will be here for you when you decide that you are ready to truly live every day and decision within your faith.