Your crew does not strike me as top-notch. It is a war, though, so more is tolerated I guess.
That's fair. The captain is an ex-Maquis, so isn't entirely familiar with Starfleet rules of conduct. The doctor is going to be sort of a Seven of Nine minus the sex appeal. Her attitude towards the EMH is an "I'm not obligated to be courteous to a piece of technology" kind of thing (perhaps mirroring Pulaski's initial attitude about Data).