How do Japanese people react to tattoos?

prohibition of tattoos is one of the propaganda (by Japanese Police) which intend to diminish the yakuza (Japanese mafia, criminal groups) power. yakuza have been squeezing money from stores, restaurants, and so on, where many people come together.
in Japan, "NO TATTOO" means "NO YAKUZA PLEASE".
ALL Japanese know this. some foolish guys have tattoos to show them be strong, by pretending yakuza behaviors.
there is a clear LINE between Japanese who have tattoos and have NOT tattoos. these two groups have never mixed together.

In Japan, tattoos are frowned upon because of their reputation with the Japanese gangs, the Yakuza. Some Japanese managers won't hire certain individuals with tattoos. However, that doesn't mean you're frowned upon. People will know you're a tourist and they'll treat you kindly. Try not to flaunt your tattoos when around others and keep them to yourself when possible. You'll have no problem in Japan as a tourist and they'll be kind, as always! Hope this helps!

I never had a problems with my tattoos, but only one is visible when I am running or working out (calf, small one).

my other tattoo is a large one, family crest on my upper back. Always hiddin. However, I have not been able to go to any beaches here because of it, but it's my understanding that the beach at Wakayama is ok with foreigners with tattoos.

Onsens? Well, I have been to a couple public onsens, and I always asked if it was ok to enter since I had tattoos. The owners always said that it was ok. "Not Yakuza" is basically what the understanding was.

In essence, Japanese people understand that foreigners may have tattoos. As long as you ask before jumping into an onsen, and are respectful, I doubt you will run into trouble.

I have to say though, that I have yet to join a gym. There's one opening up close to my school, so that will be the next test when I go there when it opens. It may be a different story at that time.

I will say that my friend Dennis, a Swede, has large tattoos on his upper arms and back. He was told he needed to keep his tattoos covered even in the locker room, but that was at a smaller, cheaper gym. So it may depend on location too.