If Judas Priest has an "official" subgenre for their classic stuff it's New Wave of British Heavy Metal, but that's too much of a mouthful. It's usually written as NWOBHM, I don't even know what people usually say when they're talking about it. And only a few of those band are well remembered, and the NWOBHM era was pretty short.
Priest had a huge influence on thrash and speed metal but alot of modern fans of those genres don't like them because they're too poppy. But they generally get more respect for people who grew up outside of that era than "normal" hair metal bands do.
Of the JP albums I like I think Screaming For Vengeance is their most hair-metallic. That's the one with You've Got Another Thing Comming on it. But when I think of Judas Priest doing "hair metal" I think of the lat '80s albums that are widely hated by people who weren't listening to what was considered mainstream metal at the time of their release
But hey, nobody's going to accuse those Halford-less albums from the 90s of being hair metal!