The original Bechdel Test essentially boiled down to "Does the novel include at least two named female characters that relate on more than a superficial level?" (Especially if they avoid a relation that only revolves around discussing men.) In other words, avoiding one-dimensional, shallow, token characters.
Of course it can be applied to any character of any minority status. Here things can get rather sticky IF multiple Bechdel Tests are required. Does every novel have to include at least two minor characters of each minority status? If done in an unwriterly, forced manner, the MS becomes crowded with inauthentic characters. Will most/all novels come to resemble each other too much? Will frankly minority stories taking place in minority neighborhoods or milieus be required to include two-dimensional majority characters? (To this I say no.) Having said all this, I look forward to that bright future where things "end up" this way due to common subconscious conviction. In this way these characters would become convincing. In today's real world, very few people are biased against people with different eye color, or handedness. Let's hope the future allows for everyone else.
Refrain: So the characters must be at least two dimensional, not shallow, but not having to fulfill the three dimensional requirement of significant change or novel length character arcs. Sans admission from the writer (a rather unlikely event), it all begs the question, how does an Agent determine this? It seems to me the only way to know would be to read the entire MS! Good!
Thus, I might avoid using any "badges" unless the MS is frankly and directly concerned with minority themes and story.
Having said all this, the obvious exception to the exception is the original Bechdel Test subject: women. The last time I checked, women comprised 51.1% of the population in the USA. You better have at least two fully realized characters who are women. Realism, anyone? I think I might even suggest, um, more...