Are modern fighter jets allowed to fly with an inoperative ejection seat?
Summary
If the ejection seat is inoperable on a US military aircraft, the aircraft will be grounded 100% of the time.  I'm sure you could come up with some weird hypothetical &quot;end-of-the-world&quot; scenario where you'd still take off, but that isn't reality today.
F/A 18 E/F Checklist Procedures
Interior Checklist
After strapping into the jet, the ejection seat is the first thing you check:

Leads, leg restraints, and harness - SECURE/ADJUST
Ejection control handle - CLEAR
Ejection control handle pin - VERIFY REMOVED

There's no point in removing the pin and checking the handle if you do not intend to arm the seats.  This is further confirmed later in the checklist.
Before Takeoff Checklist

[...]
Harness - ATTACHED 8 POINTS
[...]
Seats - ARMED IN THE FRONT
(2 seater) EJECT SEL - ARMED, AFT INITIATE


If the seats aren't armed, then the jet is never leaving the ground.  It is potentially suicidal for fighter aircraft to takeoff without ejection seats.  Fighters don't glide well (they fly to the scene of the crash), they can't fly in a total electrical failure, some can't fly without computer guidance, they can't fly with hydraulic failures, and they fly in very adverse flight conditions.  There are a lot of things, that if totally failed, would turn a fighter into a flying coffin, sans ejection seat.  Fortunately these systems are very redundant, but its usually not worth staking your life on it.