Probably tattoos matter in certain lines of work (like hospitality, "influencers", modeling, etc) where having a clean appearance would matter.
Just the same, Chinese restaurants here will employ asian-featured people to work tables. I have no idea how that works without racial discrimination being a complaint, but it is almost always a shared-race establishment. I always figured it was for "authenticity" :shrug:
When it comes to branding, we want certain models who not only align visually with the company's image, but also maybe individuals whose values or impressions fit more accurately represents their clients and their clientbase. So yeah tattoos are going to matter for certain jobs.
Discrimination happens naturally as part of business to some degree. I think most people who are the type to use the whole body as their personal canvas, they probably would not align with certain jobs anyway. They'd be more likely to enter the creative field or other lines of work where they're not public-facing... or go into business themselve as (many are doing).
Do I care if I employ someone who has a tattoo? No, not really. My clients might care if I choose photos of people with a ton of body markings for their professional websites. It would distract from their core message. Unless of course that's the demographic they are going for, relaxed, artistic, self-expressive, etc. Most tattoos though used in moderation though, they can look quite good, so I think it's quality over quantity. The best tattoo jobs are the ones I don't really notice right away, but rather I appreciate eventually as part of that's person's personality. It's easy to enjoy the craftsmanship and considered placement rather than someone covered like a mural. But that's just a personal opinion. I feel like tattoo ink can make a person look ghoulish if overdone just because of the muddy colors most people use, those charcoal blacks & blues. But probably if they did super bright colors (NOT outlined in black--that's boring) they could look quite original.
An example of beautiful tattoo work on the neck/face (not colored like I mentioned, but still good):