No, flying fighters is (super) fine... you make me smile...
What I said above is that I recommend to fly a type of aircraft that has a civilian equivalent, i.e. C-9 for the Navy, since it is a DC9.
That type of experience makes your transition into the airline world much more easy. Navy or AF
pilots who join airlines with such a background have basically a no failure record... Fighter pilots are outstanding pilots (probably "better" flyers) but their transition into transport planes used by airlines may occasionally be somewhat more difficult.
I remember having helped pilots who were flying F/A-18s in the Navy or Marines, they were outstanding pilots, but when I assisted them to pass the simulator "screening" for hire with Fedex (in a 747 simulator), they had, i.e. no concept of the use of the trim... But I believe all of them got hired.
What is more difficult, is the transition from a lightplane - flown solo - into airline turbojet equipment. Two months of initial training for new hires with a general aviation background is a tough cookie to bite. With my air carrier, getting an interview gives you a 20% chance to be selected... and if you are selected as a new hire, you have a 50% chance to fail initial training...
Sad fact... Having an ATP license, passing an interview, is NOT necessarily an open door to an airline cockpit... you have to be able to complete the training first, sometimes a little bit of luck as well, all it takes is a nasty idiot as an instructor, and... you're out.
My best wishes to you, Erik, happy contrails