Spats, I do not believe that an Equal Protection claim can succeed. Those with money will always be able to purchase things that those without money cannot. Courts usually accept that as a truism. The part that the City controls -- the license fee -- is the same for all. Making an argument that a facially neutral law adversely affects minorities because they cannot afford training costs is likely to fail.
Wally's argument bears close scrutiny. I haven't reviewed those "indecency" cases for many years, but I think they focused on the denial of the store owners' 1st Amendment right of self-expression, not the right of the purchasers to buy pornography. In the present case, the range owner cannot claim that his 2nd Amendment rights to keep and bear arms have been tampered with. So, I don't think the argument is effective, but I'd like to research it a bit.
I'm a retired lawyer. I still love an intellectual challenge and I have the time to poke around in the dark corners of American jurisprudence.