What Winkie said. I’m also in central Indiana, white, but have had no trouble in any shooting range, either.
Like most anything else, just conduct yourself with courtesy and professionalism, and it should be golden.
This may not mean what it seems to mean. The clubs around here are like that too, but if you go to one and chat with the members for a bit, it’s quite possible that a complete stranger will invite you on the spot. The purpose of the invitation rule is merely to weed out prospective members who have a bad attitude or who seem mentally unstable without having to describe in detail, in an official rule book, what exactly the criteria are.
You should also check out the Pink Pistols. They’re a group that’s all about welcoming new shooters of all sorts. I used to shoot with the Boston chapter and we had great times both at a local range and going out to eat afterwards. 