Oh dear, and I thought it was only me who was confused about hats on/off indoors!
I hadn't wanted to start the inter-service banter again but...
IMHO - The RN tend not to wear hats indoors unless they have scrambly egg on their peak, and then they like showing it off!
In the last hour I have seen 4 RAF personnel with hats on at ABW and 2 Army with berets on. Not one passing RN officer/senior rate had any head gear even with them. Because, the senior officer here at ABW says to relax headgear, I do. Personally, I'll follow that order, although some don't agree with the 4*'s drop in standards obviously
Some even feel compelled to wear their headgear inside the neighbourhoods - very smart, but is it necessary?