You have many friends here, but in many ways, I do not think turning inward is healthy. I am not suggesting you come out to them, if it has the possibility to make your life right now painful or dangerous, but often times, these people do not learn because these people have no experience. They don’t understand how widespread it is, and they speak in complete stupidity. Sometimes when they learn that someone near them, whom they protest to love, is gay, or nonbinary, they amend their opinion. That is the ideal, of course.
I don’t know how old you are, but if you are older than say, 16, I would say it is now time to begin establishing your personal boundaries. If you can do so safely, begin having, not angry or hateful reactions, but definite and dismissive responses to bigoted comments. It may even be prudent to simply say that you do not want to engage in conversations that are disrespectful to other people, and then walk away. This may earn you negative replies and consequences, BUT it is good for several reasons.
Firstly, you declare the ethical high ground, and their only possible reply is “But I want you to see how bigoted I am!” Which makes them look terrible (even to their subconscious). Next, it allows you to set a precedent of your boundaries and feelings WITHOUT revealing what you are to them. Thirdly, it requires NO EXPLANATION. You simply do not engage in cruelty or dismissive behaviors. Those are your personal boundaries. And they will either respect them or earn your disapproval. I know you may be scoffing, thinking that they are the authorities and could care less about your disapproval, but I assure you, they ABSOLUTELY care. They may not interpret it as you want them to, but ALL parents can tell when their children are disappointed in them. Recall that they are human. They had parents, and even if they agreed with their parents upon every point, at one time or another they absolutely found themselves at odds with their parents, and had to find a way.
Eventually, the hope or idea is, that they will learn to stop doing those things in front of you, but only if you handle it properly.
You must not display any sort of rage, frenetic behavior, or emotional state. Your affect should be cold, dismissive, and definite.
You should not engage in answering “Why” questions. If you interrupt their remarks with “I do not engage in disrespectful discriminatory behavior, and I am leaving this conversation” and they attempt to defend their bigotry, it stands to reason they will eventually ask what is wrong with you- a why. At this point, you have simply to distance yourself further by either repeating yourself, or saying that speaking ill of others in a way that is ignorant of their circumstances is not something you condone. The most important thing is not to use any phrasing that is “name-calling”. You cannot call a bigot a bigot. They stop hearing you. So always talk about the behavior and the aspects about THE BEHAVIOR that bother you. Give them a chance to be a better person. Give them the opportunity to qualify what they have said in a more pleasant way. If they do, this means they are aware of their fault. It makes them easier to engage. If they do not “back pedal”, then you have met a brick wall, and you walk away.
If they pursue you or belabor the point, resist the urge to engage. Repeat yourself. No matter what they say. Repeat that you do not engage in such behaviors. Find a way to leave safely, whether it be to repair to your room, or to step outside.
This is the way you teach others how to engage you. This is how you stand up for yourself and gain ground WITHOUT imposing upon them. If they continue their bigotry as a pageant to upset you, well then…
They have taught you PRECISELY what sort of enemy they are, and have made themselves more obvious. You will have learned a simple truth about your family, and that is something to confront in different ways with a separate strategy.
I am sorry you have to deal with this. But this is a plague on the human mind, one that is hundreds of years strong, but you represent a generation largely immune. Uphold that. Defend it. I know that it can be frightening (and please do not do anything that is dangerous. I cannot know your circumstances, and you know your parents.) but all of you must step back and let them define themselves. Once they have, they are easier to beat.