Out of curiosity, how does a "no politics" rule work in a scenario like this? Unfortunately we're currently in a scenario where a queer person saying they had a great time with their husband/wife/partner over the weekend can be stretched to be a violation of that rule by mean spirited people (to put it mildly). I'm not saying this is the case, but I'd personally be uncomfortable sharing in environments like that because of such rule.

That said, having a scheduled 15 minute "hello" meeting every day sounds great! I feel like seeing my coworkers and saying hi is the most value I get out of daily standups, so your team's approach sounds great to me.