I don't think you necessarily have to stop caring about what others think, especially when they're people close to you. You just need to have faith that they will act like decent human beings and just...not mind if something you do isn't exactly what they would want you to do. ^^;
Like, you're not their puppet...I'm sure there have already been situations where you've disagreed on things and kept your relationship going anyway. A good friend won't immediately disown you if it turns out you liked a movie they didn't like, or wore a shirt they wouldn't wear. Why should they act differently when it comes to your art, which is probably way more personal and important to you than any movie or shirt?
There are only two ways I can see this being an issue: A, the opinions in question concern a part of your life that they simply have NO idea about.
It happens...I've often said that no one in my IRL life really knows anything about the kinds of things I draw and write. But then, they don't care as much about my work as your people seem to...
I think in that case, I think you should think about why they don't know (is it just how it happened, or are you actively hiding things) and then decide for yourself whether this is a part of your life you're comfortable sharing with them.
If you don't want to, you don't have to. You're allowed to have a private life and keep things between yourself and specific groups of people; there's nothing wrong with that.
B, the opinions in question concern discrimination. As in, 'my family are so nice and sweet to everyone and they've always loved me, they just happen to believe that [insert minority] is a plague on this earth that doesn't deserve to live.'
As in, they could easily allow one minor detail to destroy your relationship in a way you can't predict. After all, '[insert minority] doesn't deserve to live' and 'anyone who supports [insert minority] doesn't deserve to live' is a very short leap in logic. =/
In that case, I would advise you to do what's best for yourself. If you feel like a confrontation about these beliefs needs to happen, and that you can probably handle it, then by all means...let them see your ideas and let the chips fall as they may.
But keep yourself safe...don't martyr the rest of your life over a comic; there is no shame in self-preservation. If you feel like something drastic (or god forbid, violent) might happen over this potential disagreement, just keep it to yourself, at least until you no longer have to live in that community.