Does this hotel allow people with Tattoos? I hear some capsule hotels don't allow that.
I did not see any bar on people with tattoos when I was there, and there is nothing mentioned in their FAQ. I suggest you drop them an email, I found them very responsive.
In general, if you're quiet and polite then you'll fit in well; I doubt they care about anything else, and they cater for a very international clientele so it would be surprising if they associated tattoos purely with the yakuza element.
Get an answer from Shinjuku Kuyakushomae Capsule Hotel staff and past guests.