4 cyl vtec, 98
Recently rebulit top end and had transmission rebulit.

Engine runs hot (especially when A/C is running in stop and go traffic). Removed thermostat but still gets pretty hot.

Engine cuts out at ~3800 rpm.

Compression check: all cylinders are good.

Vacuum check: good and steady

Engine lights: codes for evap system and cat. I know the cat needs to be replaced.

 

Check radiator fan operation.

BOTH fans should run when you switch on the AC.

Follow the bottom radiator hose back towards the firewall to the thermostat housing. In the T-stat housing is the radiator fan-switch. Unplug the 2-wire connector & use a paperclip to jumper between the 2 wires. Key ON, that should make BOTH fans run.

 

Both fans run with AC on.

 

Then I would suspect a partly blocked radiator.

The fans (running) should provide enough air flow when the AC is turned on. If it overheats that way, it seems like the radiator's cooling capacity is not 100%. What do the upper & lower radiator hoses feel like (hot/cool) when you just stop after driving?

Check for radiator fins that crumble & fall apart to the touch. Check for scale deposits inside the radiator water-tubes. There's some products to clean it out, but crumbling fins can't be fixed.

I'd put the thermostat back in. It helps direct water around to several places in the right proportion. Removing the T-stat altogether won't necessarily improve things.

Still.... check the fan circuit by jumpering the fan switch.
When the AC is not turned on, it's normal for the temperature to rise somewhat before the fans switch on. Normal temperature would be about 1/3 on the gauge (but the gauge isn't very accurate). It'll climb to 1/2 or maybe a bit more before the fans switch on.

 

And let's not forget the cap. If it is not holding pressure then that can cause overheating. Old days, some stores would check them, don't know if they still do since the cost of a new one is not that much. If the other suggestions don't pan out (replace the t-stat and other checks) then you might have it checked or replace it.