Hi Jessica,
I think you need to deal with a couple of issues separately. There seem to be two questions here:
1. What should you do to be acceptable to your boyfriend and his family?
2. What religion should you follow to lead a good, moral life?
Realise that these are separate questions. As Raithere said, people who really accept you for what you are should not demand that you convert to their religion, though I am not at all surprised that they might try to convince you that their belief system is a good one.
So, if you're thinking of converting to Mormonism just to impress this guy or his family, then you're doing it for the wrong reasons. If you convert, it should be because you believe in what the Mormons believe, not because you're afraid they will reject you unless you share their beliefs.
As to the second question, that is something you need to think about carefully. I suspect, though, that it is not really something you're really concerned about right now. The only way to decide which religion is best for you is to carefully think about the main beliefs of religions and work out whether you agree with them or not.
But realise, also, that you can still live a moral life and be liked and respected by people even if you have no religion at all. If you treat other people with kindness and you act morally, then anybody who thinks you are a bad person just because you're not a member of their religion is probably not worth wasting your effort on. And just because somebody is a Christian or a Muslim or whatever does not mean they are automatically a good person. There are some very bad people who call themselves Christians and some very good people who are atheists (for example).
It sounds to me like you have been exposed to quite a variety of different religions: Presbyterian, Faith Assembly of God, Baptist Church and now the Mormon faith. My advice is: go ahead and find out about any religion which interests you, but don't commit yourself until you're sure of what you're getting yourself into. If you feel like you'll be forced to accept some beliefs which you just can't handle, then don't sign up. Keep looking until you find a point of view which rings true for you. Keep in mind that that may be no organised religion at all, and realise that that is not a bad thing provided you still live a moral life.
Remember: do what is right for you, not what is right for somebody else.
I think you need to deal with a couple of issues separately. There seem to be two questions here:
1. What should you do to be acceptable to your boyfriend and his family?
2. What religion should you follow to lead a good, moral life?
Realise that these are separate questions. As Raithere said, people who really accept you for what you are should not demand that you convert to their religion, though I am not at all surprised that they might try to convince you that their belief system is a good one.
So, if you're thinking of converting to Mormonism just to impress this guy or his family, then you're doing it for the wrong reasons. If you convert, it should be because you believe in what the Mormons believe, not because you're afraid they will reject you unless you share their beliefs.
As to the second question, that is something you need to think about carefully. I suspect, though, that it is not really something you're really concerned about right now. The only way to decide which religion is best for you is to carefully think about the main beliefs of religions and work out whether you agree with them or not.
But realise, also, that you can still live a moral life and be liked and respected by people even if you have no religion at all. If you treat other people with kindness and you act morally, then anybody who thinks you are a bad person just because you're not a member of their religion is probably not worth wasting your effort on. And just because somebody is a Christian or a Muslim or whatever does not mean they are automatically a good person. There are some very bad people who call themselves Christians and some very good people who are atheists (for example).
It sounds to me like you have been exposed to quite a variety of different religions: Presbyterian, Faith Assembly of God, Baptist Church and now the Mormon faith. My advice is: go ahead and find out about any religion which interests you, but don't commit yourself until you're sure of what you're getting yourself into. If you feel like you'll be forced to accept some beliefs which you just can't handle, then don't sign up. Keep looking until you find a point of view which rings true for you. Keep in mind that that may be no organised religion at all, and realise that that is not a bad thing provided you still live a moral life.
Remember: do what is right for you, not what is right for somebody else.