Where conservative enclaves exist within urban areas, they are pretty NIMBY as well. For example, Charleston, SC south of Broad Street is plenty urban (
even has some rowhouses) rich, and Republican-leaning. It's certainly a NIMBY area as well. Lots of southern cities have urban-ish, historic neighborhoods near downtown which are wealthy, white, and fairly Republican as well.
Regardless, in my experience is people do not in any way connect their stated ideology on the national level with how they act in local elections. Conservative towns, for example, often have no problem with high property taxes to fund top-notch schools. And liberal towns have no issue setting up exclusionary zoning to stop lower-income people from moving in.