AC on 115VAC
Furnace is no problem as it runs on 12VDC and 115VAC hookup just keeps your batteries charged.
A/C draws a lot of current, but it does run on 115VAC and not 220VAC.
The standard 15/20A normal wall outlet connectors can overheat and melt over time, especially is there is not good and clean contact force.
So 115VAC is OK, but run it off of a 30A connector if you can.
Yes, this 30A is called a 220VAC connector as there is 220VAC between L1 and L2. But the AC runs off of 115VAC L1 or L2 contacts to the common ground/neutral third contact.
What the 220VAC 30A or 50A connector buys you is bigger contacts with higher contact surface and force to handle the high current the AC unit draws.
If you are forced to plug into a standard 15/20A wall outlet, then make sure the contacts are clean with good contact force and if you do not blow the 20A circuit breaker and the connector doesn't get hot, you can get buy... But not a good practice.