Well no, you don't have to respect peoples opinions. You have to respect that people other than yourself can have opinions. If you had to respect others opinions then everyone would have to "respect" the opinion that black people are less than human. Or that women don't deserve the right to do anything other than what a man tells them to do. This is an ongoing problem where people say you have to respect everyones opinion but what they really mean is that their opinion are the only one that matters and how dare you think or say anything against it.
Wording is always the issue with movements like these. If they said "sexuality" rather than "gender" we'd have a lot less confusion. But here we are.
If someone has a different opinion than you, you can either let it go or get into an argument. You either agree to disagree or you have a war back and forth trying to convince the other person. You gotta decide whether its the hill you wanna die on or not
Hence, why I said you have to respect that people other than yourself can have opinions. There's a big difference between respecting that people can have their own opinions and respecting their opinions. The later, much like the right to free speech, means people can say stupid things and believe stupid things but you're allowed to call them stupid. Whereas the former, means they can say those stupid things or believe them and you have to "respect" those thing as just as valid as your opinions.
If someone has a different opinion than you, you can either let it go or get into an argument. You either agree to disagree or you have a war back and forth trying to convince the other person. You gotta decide whether its the hill you wanna die on or not