It is often portrayed like an old-school hackerspace or makerspace but it's definitely not. It has an explicit corporate background, and it always feels like that is somehow hidden. In these comments there is a comment that claims that RC is not for business builders and networking, then immediately gets disproven by a quote from its very website. This shows that you have an actual image/brand problem.
It is similar to how the term "hackathon" evolved. In the old times it was people coming together who worked on shared goals (like a FLOSS project) but only communicated via mailing lists and probably would never met in person otherwise. A hackathon was often an emotional thing, involving poor people travelling to the other side of the planet to meet their online friends to drink beer and finally have a whiteboard to communicate some complex ideas. Then corporations came and organized soulless "hackathons" and turned it into an idea farm and talent recruitment. The term "hackathon" is pretty much burnt completely nowadays.
So anything that feels like it gets subtly used by corporatism just naturally gives techies the ick. It is not the first time this bait-and-switch happens, so people are fair to assume intent.
I say you cannot control it, as obviously the public image comes from those blog posts of RC "Alumni" (Another great example: that term alone gives me the creeps). And those people have the right to feel excited about a nice experience that it probably was for them.
But Recurse Center should probably be proud of the corporate background and actively counteract the impression of being a hobbyist makerspace that just has better inventory and manpower.