Ask them if they would still like you if had a different favorite color than them. Or what if you liked two different colors? Colors are all colors, but they are all beautiful. People are the same way. We're all beautiful. You like a different gender than some people? So what? It makes you happy, so why should they care?
From this, I'd assume that you're a part of the LGBTQA+ community but if not, I'm terribly sorry for this unrelated response. Homophobia is ignorance and fear. Fear is very strong and it can be hard to overcome, especially since homophobic people think their hâte is legitimate. If you're underage and supported by them, the consequences could be too risky if you came out right now. You depend on them financially and you wouldn't want to lose that, even to express yourself to them. If you aren't, you're an adult, you can try to educate them on the subject, try to dissipate their ignorance and, eventually, their fear. Best of wishes :)
Okay, I believe that what really helps solving a problem is talking it through. You can talk about it with your parents, and eventually they will have to accept you and your choices the same way you accept theirs. If your parents won't listen or won't stand a converstation like that, then you could talk to a trusted adult and figure out a solution, but talking with them and letting them know of how you feel is an important step. All parents should love their kids for who they are; and that's for things they agree to and things they disagree too. My best wishes and I hope dealing with them goes well!
The best way to deal with homophobic parents is to educate them. One of the biggest reasons for homophobia is lack of education about it. In the end, you are thier child, they will always love you. You just have to remember to be patient and understanding of their confusion and possible hurt. You aren't doing anything wrong, they just have to process the lifestyle change themselves, just like you did.
It depends on many factors, including your relationship to them. The first rule is always to put your safety above everything, so if you don't feel safe you should do whatever you can to protect yourself. If you feel safe but still don't think they'll accept you, it's up to you to decide what would make you feel better: the comfort of not opening up, or the comfort of being free to express yourself. If you decide to open up, it's important to try your best to discuss openly why they are against it, and face their arguments one by one by providing logic reasons to dismantle them. you can also provide them with some good resources, also scientific and academic texts, so they can learn more from sources they can find reliable. One more thing that is very important is to get support no matter what. If your parents won't accept you, you can try to open up to supportive friends or to some LGBT group near you. You deserve a chance to openly express yourself with people who support you and accept you for who you are. Support always makes us feel stronger.
When I was younger my mother never accepted the fact I was non-binary because she was homophobic, but if you keep it a secret it makes it stressful and letting it out gets you in trouble, so try to talk to someone who wouldn't leave you and tell them your problems and when you're confident enough tell them.
The answer depends partly on if you are gay/queer or not, but generally I would say be patient but strong in trying to show them that homophobia is not acceptable and that there is nothing wrong with gay/queer people.