1) option for large groups (around 250) This drops Signal out which has a limit of 150 on groups: https://support.signal.org/hc/en-us/articles/360007319331-Gr...
2) e2e encrypted (because it sounds good, not because people actually understand what it is), including groups. This drops Telegram out: no e2e rooms.
3) handles sending photos, videos, and voice messages. More or less kills XMPP, unless people are on the latest-and-greatest version of Conversations and maybe ChatSecure.
4) the maintaining organisation needs to be reasonably big with decent privacy.
5) usable for completely non technical generic population - meaning Tox is out as well.
As much as I dislike to admit it, this leaves Matrix, and nothing else. My problem with Matrix is that it's so resource hungry - both the servers and the clients - is that it's silly. Yes, I know "optimization is coming" but even Dendrite eats 1.5GB memory easily with a single user joining a few, medium sized, federated rooms (yes, I've tried).
Footnote: Threema... no. There is no need for yet another competing open source thing, there are enough with Signal, Matrix, and XMPP.