Hollywood.
View attachment 538
Real life. Tattoos and heads are blurred. The White House didn't blur them in the original post, which was a huge blunder and probably made these men have desk duty till retirement.
As far as I know, there are no regulations on tattoos for Special Ops. They cover up, for the most part, when going in, so they can't be identified and put on lists. If you think of it logically, it's kind of good to have tattoos or identifying marks in the event that they're captured (or worst case, and the only thing left to identify them are marks).
I know quite a few recon guys with tattoos too, but they aren't under SOCOM. That said, I'm unsure whether SOCOM has new rules and regulations and these men were grandfathered in. Tattoos weren't an issue in MARSOC in the mid-2000s, which was folded into SOCOM later, so that could very well be the case.
That said, it would make sense for CIA to not have tattoos. Though, I don't know much about them, and don't want to.
This is what ChatGPT had to say (with official sources cited, but stripped for the sake of this post):