Well, conservatives in the US have thrown in with a party that typically demonizes people of color, is actively working to disenfranchise them, and has a growing white nationalist element to it.
Are there some conservatives who really just care about there being too much government regulation, or whatever? Sure. Looking at the party they rally around and the way it wants to treat people, there sure are some general trends that do not speak to a desire to embrace diversity.
There's a difference between being a Republican, and being a Conservative. To that end, the Republican party itself is not the monolith that you see in the Democratic party. There still exist factions that resulted in the passage of a lot of Democratic policies while the Reps. controlled Congress during the last presidency.
While I don't support the Republican party, I still hold conservative ideals, primarily regarding regulation and oversight. My social views are fairly liberal, but I don't identify with the progressive movement and intersectional politics.
EDIT: I think diversity is great, but diversity as an end goal is misguided.
TBH the other side is kinda big on demonising people of certain color, sex and sexual orientation too. The whole identity politics thing is disgusting regardless of vector.