Actually a very hard question with a million answers for a million different combinations of identity and scenarios.
At a high level I think recognizing validity takes the form of a social acknowledgement that someone else as "as much" right as us to be in public space. You can think about LGTBQ+ folks going out glammed-to-the-gills, or how the modern gay rights movement started after police raided a gay bar for no particular reason, or slut marches protesting sexual harassment. These are all people doing things in public that are taboo in a way that's related to their identity (gay people acknowledging their sexuality in public / people dressing in revealing ways) and demanding they be treated with respect. Often even if they are shouting rude things.
For a more heteronormative example you could think about the distraught parent who might break social norms when their child is hurt or killed. If you're a doctor and you have to tell the parents their child is dead and they scream at you, you don't treat them like they're random people on the street. You respect their validity and understand that they are dealing with a lot and your feelings aren't top of mind[1].
It can also be as small as not asking where someone who is a little racially ambiguous "where they're from" before you get to know them. Not because the question is rude exactly, but because it's probably a question they get a lot and it highlights the difference in your backgrounds.
[1] This is actually very hard on medical professionals even if we all understand!
I personally think that, besides the above, a lot of the loudness comes from a feeling of freedom. Where all of a sudden you no longer need to hide who you are, which leads to a stronger expression of a part of you that was pent-up.
This means things like recognising that being gay is a thing, that it's a normal and perfectly ok way to be, and that the person in question is in fact gay and accepted into the group as such.
It's the opposite of the kind of parenting that makes people nervous to "come out" (which many gay kids will have grown up in).
Can this get expanded on a little bit? How does one recognise some else's validity?
I get the simultaneous feeling that leaving them alone isn't what they want, and me waving my hands and pronouncing them (eg, a young gay) valid is likely to get a very negative reaction. Who am I to decide what is and isn't valid. What exactly does that mean in a what-do-they-want sense?
My guess is they want other people to copy them so they can build a community, but I'm sure there are other interpretations.