I think this is crocheted hat, but as I'm neither a knitter or crocheter, I'm probably wrong.
The hat is not very stretchy but still fits well and is very comfortable to wear, the sort of hat you could wear all day without noticing.
Not following a particular religion this is therefore not something I would wear socially, so for Larp use only.
The cross crosslet in the design of the hat is not associated with any particular Christian religion, at least as far as I can tell, its more associated with the spreading of Christianity, i.e. its also called the missionary cross.
The hat has 2 little toggles hanging from the centre button, if anyone knows what they are called I would love to know.