CMOS latchup these days is usually >100mA, and you'll be hard pressed to draw more than 10mA from a coil that idles at 10mA. But YMMV. A lot of MCUs don't spec it.
Could even wire it between two pins (H-bridge drive), to speed turn-off. You'll have to know the inductance though.
Schottky clamp diodes won't hurt; a BAT54S per pin will certainly do.
If you need the assurance of a proper spec'd logic family, 74HC3G14 or the like would be a good idea; wire all three sections in parallel to get extra-strong drive. (Or use a 2G or 1G part and only as many as you need. One should be enough, after all, but you can also overkill if you like.

) The output transistors will handle that current with very little voltage drop indeed, and the CMOS latchup rating is given either in the datasheet or the logic family sheet.
Tim