Nothing to add to the excellent regulatory explanations above. Any Cessna can dribble through any time it wants to. And (if under VFR) is free to contact ATC or not, and if so, to follow ATC’s advice or not.
As a practical matter, the majority of MOA airspace is lightly used by the military. The main exceptions are those surrounding the active duty pilot training bases.
Someplace like CATO or SMITTY used by the ANG probably gets very little use M-F and may only have a handful of jets in it all day during the weekends. In some ways the Cessna is safer in there than he would be outside the MOA just because so many other VFR slow-movers will choose to avoid MOAs on principle. Most times he’ll have the sky to himself. But if he doesn’t …
Despite Broomsticks’ contention above, IMO both airplanes are probably junk if they collide. At least the fighter pilot has a decent chance to jump out if he/she wasn’t killed in the immediate collision. The Cessna driver is almost certainly doomed regardless of the details. Absolutely aircraft do occasionally survive mid-airs and land safely. But it’s sure not the way to bet. Gol Transportes Aéreos Flight 1907 - Wikipedia
A practical problem with mixing slow-movers with maneuvering jets is the speed difference means a jet can run down a slow mover from any direction in the sphere: from straight down, straight up, above, below, behind, head-on, you name it. Even the most diligent slow-mover pilot with even the best of bubble-canopy outwards visibility simply can’t see and avoid all the potential threats from all the potential directions. Joe/Jane Sleepy Private Pilot in their Cessna doesn’t stand a chance of spotting the light gray dot that kills them.
Conversely from the fighter’s POV if you’re at speed and about to hit a slow-mover it’ll have been within ~10 degrees of your nose the whole time (net of your manuevering). Radar is helpful for spotting targets there, but depending on what else the fighter is doing the pilot may not be looking at it or be in the right mode at the critical time.
In the course of looking up the details on these particular MOAs I see the ones dedicated to Williams AFB, the pilot training base on the east side of Phoenix, are still in existence.
Willy closed as a USAF facility in 1993. 27 years later USAF hasn’t given back the airspace. And probably never will; there’s simply no way to ever regain it.
As to drones and the OP’s HOA, that seems like a convenient excuse rather than a reason. By FAR drones are restricted to at/below 400’ AGL. The SMITTY MOA extends from 500’ AGL upwards, with CATO piled on top of SMITTY at even higher altitude… So all (legal) drone ops would be outside the MOA anyhow.