Q: Can the replacement of the ignition switch cause the air conditioning to stop cooling?

Hello. To replace the ignition switch, the Technician would have been "near" the dash. The only possible connection would be if he did something to block or de-activate the air passages, blend door, or related controls or the A/C. If your problem is that the VOLUME of air is "lower", rather than the temperature of the air is higher, that is really the only possibility and even that is unlikely. Other than that remote possibility, there is no other possible connection between changing the switch and the A/C problem you are describing. So, if the air volume that is blowing now is the same as before but the outlet temperature is not low enough, the system is possibly low on refrigerant charge (could be other or additional causes) but that has to be diagnosed and verified by an A/C specialist. Such a specialist from YourMechanic can come to your home or office and diagnose this air conditioning issue and repair this for you.