How do my feelings inhibit other people's rights if I don't physically do anything to them

Not one's feelings specifically but actions in general. IE: KKK believes whites are the supreme race, and they have all the right in the world to believe what they want, it's why they can have police protected protests. But if they started tying actively trying to keep minorities out of upper end jobs or positions of power in the economy, that's when they're inhibiting another person's rights. Technically though as you said, their feelings '[b]should not[/b]' under any circumstances be made more vital than those that don't like them. Feeling alone should not validate being 'oppressed', nor, in my earnest opinion, should a single case of possible bullying or name-calling, but laws in place that restrict said group from things that other groups have access to.

How are there laws restricting trans people from doing what they want

I believe in the sense of laws that would bind genders respectfully, IE: A Male in many states cannot enter a Public Restroom for women, however in some states like Maryland if you identify as female despite biologically being male you're permitted use of female restrooms. Other arguments are that men who identify as women aren't allowed, or aren't supported, being in female-only sports leagues. They want general laws and policies that make it so the fact they are transgender doesn't limit them in any way as far as having regular lives that won't interfere with their identification. Most of the complaints(as far as I'm aware) from the community are less about laws 'persecuting' them as much as they want people as a whole to be more accepting of them and the idea of transgenders, much of these complaints are often blown out of the water as far as how much they are truly being 'persecuted. At least this is my personal understanding, no expert on it in any way.

I think people should use the cards they've been dealt (ei their gender) there are many things people aren't happy with in their life, deal with it

It's an interesting subject as far as how much it's discussed, I wonder if anybody will ever identify as a different ethnicity or race under the terms of being given the wrong body.