I'm wondering if a modern fighter jet (Eurofighter, JAS Gripen, F-35 etc.) is allowed to fly when the ejection seats are known not to be in working order.
That will vary very much from country to country. While civil aviation regulations are very much standardised across the globe through ICAO (of course with local exceptions) and manufacturer's guidance, military aviation is very much the domain of national regulations.
Technically a military jet will be able to fly with an unserviceable ejection seat, so I imagine that some countries under some circumstances allow flying when they don't work.
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 "end-of-the-world" scenario where you'd still take off, but that isn't reality today.
F/A 18 E/F Checklist Procedures
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.
I asked some of the fighter pilots that I know, and they couldn't give me a concrete answer (for the USAF), and I couldn't find a regulation that states it is grounding. However, I'm sure it would ground the aircraft.
In this instance, fighter jets (F-35s) were grounded for a "relatively" minor issue with the seat:
Fifteen F-35 Joint Strike Fighters will remain grounded for at least five more days because their ejection seat parachutes were installed backwards
Even though the parachute was packed backwards, it still would have deployed, but the steering levels on the parachute would have been reversed, making it confusing for a pilot to steer
Key note there is confusing for the pilot. The ejection seat was functional, but the fact that it was confusing was enough for it to be grounding. Possibly in wartime it would have been different, but I doubt it.
And even in the case that it wasn't grounding, there's no way I (or any of the pilots I talked to) would take that aircraft. It's not worth it.