The gun "clubs" require an NRA membership and usually a panel of whatever 65+ yr old boomers are members to decide if you are a "good fit" for the club after some probationary service period. This seemed pretty standard across the 5-6 diff clubs I looked into initially.

Having shot at several of the clubs during some pistol league competitions, I was not optimistic that someone openly gay/trans/ not white would have an easy time getting membership (totally an assumption, possibly an unfair one). Combine that with having to be an NRA member to enroll and I didn't bother.

Indoor ranges (not gun clubs) around the state don't force you to have an NRA membership. There is also the Great Swamp Range in S. Kingston area that is free, but its only open from April to late October. You have to submit some paperwork that is a bit slow so definitely get in there. It's a very nice outdoor range and often not crowded at all.