It's not all that rare for enlisted men to apply to and get accepted to OTS. And the switch from Marines to Navy isn't uncommon either. Now a switch from Navy/Marines to Army or Air Force would be strange.
Ooops. Make that "OCS".
I was assigned (MI) to SF during Vietnam and there were several former Marines in our group. [HATED trying to march with a Marine calling cadence.]
And, note to an earlier post: yes, Martha Raye was a legend for her service.