Unistall and Install over the range microwave
While I cant speak to your particular microwave or cabinets, there is an issue with many setups that do require an angled entry that may be the problem the installer is concerned about.

Many over the stove microwaves hang on a metal frame attached to the back wall. This frame usually has a lip at the bottom that engages with slots in the bottom back of the microwave and provides the support at the back edge. The other support points are bolts that come through the cabinets near the front of the microwave.

The microwave needs to be tilted on about a 45 degree angle to engage that back lip. Once engaged, the microwave is then tilted up and back until it is flush with the wall ant the bolts can be dropped in from the cabinet above.

It may be that the existing molding will prevent that tilt. The above cabinet prevents the microwave from being lifted straight up to clear the lip.

I would remove both inside (both sides)and front trim, and then reinstall after the oven is in place.