To be fair I don’t think I really pass as a cis woman. But again, I had no issues except for the usual few odd looks from a minority of passengers.
You should both do it! It is a great experience
The UK and RoI have a treaty known as the common travel area that long predates the old EU free movement and a passport is not required to travel between them – just ID – but you do still need to go through customs. The Irish border guards do like to check the ID, however, and I believe there are not the volumes of internal flights to allow an airport like Dublin to justify having the ability to filter passengers through different corridors so that they skip passport control but not customs.