That's an interesting question. The short answer is, yes, I use metric taps in them. I have not had issues with the fit of metric taps.
There are standards for tap shank size and square drive size. So, if the taps are made to the standards, they should fit correctly. Well, maybe. See there are several standards for tap drive dimensions. There are standards dictated by ANSI, ISO, DIN and JIS, and of course they don't always agree with each other. DIN has seven different standards that I'm aware of. The bad news is that all these different standards seem to complicate things a bit. The good news is that many of these different standards use the same (or very similar) drive sizes. I found 37 different standard drive sizes for taps up to 1/2" and 12mm. However, several are within .005" of each other. A size difference this small is insignificant in this application. Lisle makes 8 sockets to cover the same range of tap sizes. This set covers the ANSI standards.
Now, we should get back to the practical side of the issue. Just for fun, I measured the square drive about 50 of my taps. All were within +.002/-.007" of the ANSI standards. As far as I'm concerned, this is not a problem.
