Are they? Looking at the polls[1], it's not really clear either way. For instance much more republicans think that "the state of moral values" is a "big problem", which seems to suggest they're "more interested in culture wars", but at the same time for "racism" the numbers are flipped.
[1] https://www.pewresearch.org/politics/2023/06/21/inflation-he...
It's trivial to reword this for "the state of moral values", eg. "we are currently in a place of degrading moral values, and anyone advocating that moving away from that place is bad, happens to be advocating for degrading moral values indirectly". In other words, both "racism" and "the state of moral values" are culture war topics, and I don't how you can justify privileging one without having to invoke your own political beliefs.