What does "diversity has more of a purchase" mean?

The following is an excerpt from the Japan Times article of June 15 regarding "hikikomori" (social recluses).　

According to U.S.-based journalist Makiko Iizuka writing for Yahoo News, new labels are always being introduced in Japan and they invariably create negative stereotypes: “parasite singles,” “freeters” (young part-timers who are not students), “hinkon joshi” (destitute girls) and so on. News outlets cling to these terms “with a sense of titillation,” she writes, making them “trendy” and establishing them as behavioral predictors that exacerbate prejudices. Such labels tend to be suspect in the U.S., where 〈diversity has more of a purchase〉. In Japan, however, the public is receptive to them, and they are sometimes used to describe people who may not display many of the attributes affiliated with a particular label, if only for the sake of convenience.

What does diversity has more of a purchase mean in this context?

Solution 1:

As @tchrist suggests, purchase has a meaning that, while familiar to most native speakers of English, is far-removed from the more common meaning. Oxford/Lexico:

[mass noun] Firm contact or grip.

‘the horse's hooves fought for purchase on the slippery pavement’

[in singular] ‘an attempt to gain a purchase on the soft earth’

"Diversity has more of a purchase" is saying that the concept of diversity has "taken hold" in the US more than it has in Japan. It's not a particularly idiomatic use of the word, but its meaning is reasonably clear to most native English speakers.