It depends on how fluent you are and if you have an "American" accent. Or if you have a Japanese name.
As a general rule, the shops know that customers want their hobbying to be on the down-low so don't ask to see ID by default, because people don't want their real names associated with their fun. So they'll only really probe if they suspect something.
I have a friend who's Japanese-American but speaks with a very American accent. But he has a drivers license with his Japanese name in Kanji, so even if he gets questioned he just pulls it out and gets let through. Or he gets turned away sometimes based on language ability, in which case he just finds another shop and tries again.
On the other hand, I don't have a Japanese name but my accent is pretty hard to pick out. So I get into a lot of No foreigner shops without paying gaijin tax. One of the things I've found is that the really strict shops look for mannerisms - whether you bow, the way you count money and hand it over, stuff like that. If you've lived in Japan for a few years you'll probably have picked up on enough of that to blend in.
If they suspect you, all that will happen is that they will ask "ę„ę¬ć®ę¹ć§ććļ¼" and if you don't feel like lying, just say no. Or you can say that you're ćć¼ć and your mom is Japanese, so you don't have a Japanese surname. They'll either turn you away or ask for gaijin tax. Or they might test your language ability and just let you through. Either way it's no harm, no foul, no hard feelings. Don't think too hard about it.