I've never had a problem sharing it. And no one outside tech has ever brought up BDSM when I tell them about the program or help them install it.
An extremely conservative church group is perhaps the worst place to try to figure this out; y'all will self-censor naturally.
Anyway, I teach IT, in a department -- shared with Communications -- and can absolutely assure you that this name is a no-go. I get that people don't like "politics" and "optics" and such, but that's what's happening here.
If your department wouldn't use free software because of the name, that's very much a them problem. And it's sad that they're so sensitive.
If you don't like the name, you don't have to use the software. Or fork it can call it something more anodyne to your sensibilities.
But no. You want everyone to cater to sensitive people. And thus, myself and others are here to say your comment is annoying when this comes up every thread that GIMP is mentioned.
There's really no "shut up and go away" that you can give me that will work, because you aren't some grand FOSS arbiter, you're just some rando on the internet like me.