I haven't read any of the other responses and I'm rather late to this discussion but here's what I think. Feel free to object to it LOL.
1. You asked, "Why should I respect other people's beliefs?" The reason why it's considered common courtesy to respect another individual's religion/beliefs is because it's a very touchy subject and frankly most people are going to stick to what they believe and not going to change what they think for anybody. But the reason I think that we should respect other's belief is because it's just that - their's! We don't have to believe it and we don't even have to like it. But whatever religion (or non-religion if you're an athiest) they choose is their business and it's their life and we should respect their decision. I know that I wouldn't like it if someone started arguing with me over my religious decision. I'm a Christian and I'm not going to force someone else to be one but I would want them to respect my choice. I don't necessarily agree with other religions such as Islam and Buddhism but I'm not going to criticize someone who has chosen that religion for their own. I think this way with sexual preference as well. I'm a straight female and I probably always will be but I'm not going to look down on someone who is a homosexual. That's their decision, their life, and who am I to judge their choices? The only beliefs that I will not respect are the ones that harm others, mentally and physically.
2. I believe that there is a flat-out right and wrong but I also believe that there isn't. As our world as a whole, no, I don't believe there is a plain straight Right and a plain straight Wrong. Why? Because everyone thinks differently and I'm fairly certain that there isn't a single issue in the world that everyone fully agrees on. But as individuals, then yes there is an objective right and wrong. I, for instance, believe that rape is wrong. But you have others out there who don't. Our society and culture have deemed what is "right" and what is "wrong" and that is what most considered the norm but you will always have people who disagree and it's alright to disagree. But once again, I don't think it's okay to harm others. I would never think that rape is right.
3. I do think that everything has an objective answer but most people never want to discover it since it would take much too time and effort and in some cases, research and experimentation.
4. You say that you're tired of people disagreeing with you and saying "that's my opinion?" So what do you want? To convince everyone to agree with you and take up your opinion? For everyone to agree with every little thing you say? Opinions are what make this world go around. It would be a pretty boring world if everyone thought the same. Everyone would be like robots. You know what's funny though, is that you say you think it's lame when people use "It's my opinion" as their defense but I honestly believe that even if they did have reasonable evidence to support their side, you still wouldn't agree with them. It's human nature - we're defensive people. We have our opinion and we stick to it, sometimes even when we know we're wrong!
Anyways, I'm sorry about whatever provoked this! I've felt like this before so I'm sorry if at any point in my post I come across as harsh or condescending!