Available power is marginal so whether main breaker trips depends on specifics. Obviously not all microwaves or A/Cs are the same or pull the same current.
Typical RV microwaves in the 1,000 cooking-watt range can pull 13 Amps easily. Mine did. And with air conditioners there is an even wider range of power. High efficiency 15k BTU/hr units run at less than 15 Amps under standard conditions, but less expensive units often installed by manufacturers can easily go over 15 Amps.
To make matters worse, in very warm climates air conditioners pull more power/current. Warm temperature inside and or outside makes A/C work harder, making it more likely to trip breaker. A/C manufacturers list extreme of this information under desert conditions.
Low campground voltage may also play a part. The difference between 110 and 120 Volts can be significant.
And as others have said, other loads like water heater or converter charging batteries can take total over 30 Amps.
On a cooler day after motorhome has cooled down, turning the microwave on for a few minutes while A/C is running "should" be OK most of the time. I've often gotten away with it. On hot days when inside of RV is still warm I usually turn off A/C first.
Likely outcome is not black and white in my opinion.