What do you base this idea on?
I work in the arts/entertainment industry. My wife and most of my friends work in arts/entertainment and/or in academia related to it.
I grew up very conservative (I did a presentation about Rush Limbaugh in 8th grade and also caught the tail end of the Satanic Panic); my family is still very conservative and I'm very familiar with the rhetoric that permeates that culture and the media pundits who influence it.
IME, being effective in the arts requires a level of curiosity, empathy, understanding, and comfort with ambiguity (particularly moral ambiguity) that is extremely hard to find (and often discouraged) on the right. It also requires treating art and practitioners of the arts with some measure of respect and thoughtfulness, yet my entire life I've watch the far right denegrate the entire industry and everyone in it as a bunch of godless, liberal heathens and their work as trash to be burned in the town square.
Your side can't be effective in an industry that you train your children to despise and distrust. Few of them will be inspired to enter that field in the first place, and those who do will be at a competitive disadvantage because they'll have to unlearn all of that nonsense before being able to do the work.
Federalist and National Review are read by the rank and file and they do have arts coverage, so does Reason Magazine.
I wasn't aware of this, so I did some looking.
I went back through about a week and a half of Federalist posts and didn't see much beyond reviews of GoT or Marvel movies. (given this week's lineup, that's not surprising and FWIW I don't necessarily fault them for that) Some were stupid; some were fine, but not terribly thoughtful. None of it was inspiring. But even assuming that there is some good, legitimate, thoughtful art criticism and understanding buried in there that I just didn't find, getting there would've required wading through tons and tons of simple-minded, dishonest invective (in the form of their other articles) that is entirely antithetical to creating good art. Any prospect of engendering art appreciation in a single piece would've been undone by the dozens of bitterly negative headlines past which you would've had to scroll to get there.
National Review was notably better, but they're sort of the last bastion of Never-Trumpers, so I don't know how representative they are of the whole of the right. It wouldn't surprise me if there's a high correlation between being a never-Trumper and appreciating art. Ditto for Reason. I didn't find much on Reason aside from their TV section, but they strike me more as sensible libertarians than as hard-right antagonists a la Hannity et al. They would be the places I'd expect to find Koch and the other remaining rich art-appreciating holdouts.