Do you care about abortion rights?

That they are viewed as rights is cultural.

Do you care about refraining from torture and genocide?

That they are viewed as abhorrent is cultural.

If you carefully define culture as to be everything that doesn't actually matter, then what you say is true. But I think there are plenty of aspects of culture as typically construed that impinge upon well-being that you probably aren't willing to sacrifice to whomever wants it to go differently.

I'm certainly not willing to give up everything that is arguable on the basis of culture. I have pretty clear views on some things. Abortion rights yes, torture no, genocide no. And if people think differently, too bad for them, because their fondness for a way of being does not give them the moral justification to harm and control others to that extent.