That isn't what the research you linked shows, though! The research only shows that white men are nervous and underperform if being pro-diversity is prominently announced vs. not announced.

It doesn't explore why.

It might be that they think leveling the playing field works to their disadvantage.

It might be what they report when asked: they think they'll be discriminated against. Not level!

It might be stereotype threat ("everyone knows girls are bad at math, I mean, everyone knows white men are not diverse, but they want diverse").

It might be other things.

The study doesn't probe the possibilities.

However, I note that by assuming the worst reason despite it not being tested, you as a hiring manager would validate at least their stereotype threat, if they feel it.