The good news for gay men? A new analysis of U.K. data shows they are more likely to be supervisors and managers than their straight counterparts.

The bad news? Gay men are far more likely (7.9 percentage points, to be exact) to be stuck in low-level management jobs at the bottom of the organization chart or at smaller, less prestigious organizations — the shift manager at a retail store, for example. They’re significantly less likely (2.2 percentage points) than straight men to be high-level managers — the people who run trading floors and manage entire regions.

The worst news? Gay men of color are hit hardest. They face an even worse disparity than you’d expect based on adding the gap for gay men to that for men from racial minorities...