I don't see the issue.
Picard and Crusher referred to each other on a first-name basis. Sometimes Picard called Riker 'Will' and La Forge 'Geordi'.
I've never served in the armed forces, but even from my perspective I wouldn't deem it offensive. If I were a new sub-Lieutenant in the Royal Navy and the CO of my ship and the chief engineer had known each other for 15 years prior, who am I to complain if they call each other via their first names instead of "Lt. Cmdr"?