Ah, I disagree. I think that we'll be moving in the right direction when political parties stop trying to appeal to people of a certain colour and try to serve their constituents in the best, fairest way possible. We can't decrease our focus on race by focusing on race in new ways.
So, yeah, I don't thnk there is or should be a "conservative stance on race". Just as there shouldn't be a conservative stance on feminism or LGBT rights or religious freedom. The woke left's hyper-focus on these issues is as unhelpful and divisive as the right's disain. Just in different ways.
I consider myself left-leaning (as opposed to woke left) because I think the priority should be fairness. I think the priority should be treating all people with dignity and respect. I think the priority should be helping those who need help and making sure everybody gets a fair shot. If we get that right, all those other differentiators become unnecessary.