Overheats unless ac is running

check fluid level --fan working correctly--water pump working -radiator clean

have a radiator shop check for blocked cores
have a compression test done
water pump not an issue unless you have removed the ac compressor out of the system and now the water pump is being driven in reverse because an idle pulley was not used in place of the compressor

I'd look at a leaky head gasket, which causes persistent overheating. There is a simple test for this, which any mechanic can do

https://www.youtube.com/watch?v=a3J00_e7fyo

https://www.youtube.com/watch?v=g5Hbweydb3s

https://www.youtube.com/watch?v=888jdjVXP80
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check the cooling fan it should be on when the ac is on

You need to change the "Coolant Temperature Sensor". That usually controls the fan. If the fan does not run, you will overheat.

the fan speed is variable to save fuel, the fans don't run unless the engine gets really hot, about 230 F, that is well past the middle of the gauge if u havce one, so the fact they run with the AC on means the system is almost certainly functional as long as u are not showing an engine overheat, are U?

It sounds like your AC compressor bearings may be overheating causing excessive drag/loading on the engine. No easy way to check this unless you can take the serpentine belt off when the car won't start and see if it is really hard to turn the compressor shaft.

since the water pump was replaced, make sure you don't have an air pocket in the cooling system. flush your cooling system again. remember, if all was well before the tune up/preventative maintanance, it's within those items that were replaced. I don't think it's the condensor, thats a/c related, but the radiator and water pump, well those can cause overheating problems. when the system overheats, you will feel it in the ac.

Couple of items you need to check. Make sure that your radiator is flowing properly. Often after sitting dry, blockages harden up and flow less than before, overheat originally before repair can also free up debris inside engine and add to plugging of core. Make sure that fans are operating especially with ac on. If you did not change thermostat during repair, change it. Not often but they can sometimes partially open, restricting flow. Also make sure that coolant is at correct concentration (50/50) and that there is no air trapped in the system.

check the water pump