Well, first of all, welcome to the forums!
As for your question, well it's difficult to give advice on that because every person and every situation is different.
Some general advice would be:
1. NEVER compromise your morals, values or beliefs for the sake of unity. However, you also need to learn to pick your battles. You can always agree to disagree and be friends with people despite your differences. GOD brings various people into our lives for a reason, so you don't want to destroy relationships over political or religious arguments. Just let them know your beliefs and try to be a positive influence in their lives. It might take years but it will have an effect on them.
2. Try not to get emotional, when this happens your argument loses credibility. This is obviously extremely difficult, because if you aren't passionate about something, then why even fight for it? You just need to temper your passion with knowledge, because passion without knowledge simply leads to extremism.
3. Learn. Learn everything you can about your beliefs and try to understand WHY you believe the way you do. Also try to understand why those with opposing viewpoints believe the way they do. Try to anticipate every possible argument against your beliefs and also try to recognize when the person you are arguing against has become irrational and then exit the argument as soon as possible. Usually people get irrational when they are backed into a corner. One sign of this is they constantly change the topic. YOu might be talking about gay marriage, then they suddenly make a statement about assisted-suicide, when you try talking about that, then they suddenly want to talk about gun control. When this happens, then just stop debating the person and either talk about something else or leave them alone.
4. Start small. You can't change the whole world right away but try to make a difference in the lives of people that GOD brings you into contact with.
That's all I got for now, maybe someone else can add to it.