Theatre careers are full of these awesome trade-offs.
You can have Integrity and only work on interesting, original, thought-provoking shows and shiver at the sheer artistic quality of every project you associate yourself with. You might succeed and become a Great Actor/Designer/Director/Technician. You'll probably spend a few years doing indie theatre and then have to leave the industry. And if you decide that that's a risk you want to take, and that's a lifestyle you want to live (To misquote a retiring life-long RSC company member: "Dame Theatre has never provided me with wealth or celebrity, but she has always kept a place for me, and for that I am eternally grateful."), okay. Go nuts.
You can also sell out. You can take the industry shows and work on cruise ships and accept contracts for work which you know is going to be trite and uninspiring and derivative and sappy and which you might even be a little ashamed of--but which will always pay the bills and provide a little more. And instead of taking pride in the quality of your CV, you can take pride in your employability, and in your (relatively) solid career, and in the non-theatrical (or, indeed, theatrical!) pursuits which that little extra income provides for you.
There's nothing "right" or "wrong" about either of these approaches. You aren't a better or a worse person for pursuing them, and the industry probably needs a certain number of people who fit in both camps. Most of us don't even fit neatly into one box or the other.
And tattoos are on the same basic matrix.
Getting visible tattoos will limit your career options. You should still be able to find work, but if you plan to get to a level where you're regularly working with people who wear suits and have private offices, you may struggle if you have visible tats and unusual piercings.
If you want to get to that level, then this is something to consider.
But if that's not a life you want to live, and that's not somewhere you can ever see yourself being happy, and you prefer the lifestyle associated with "lower-level" work, then go nuts.