@John Tarricone Well here's my opinion. I have a duplex where the previous owner painted over the gorgeous millwork in the downstairs unit but left it original upstairs. This is not your standard colonial moulding. And let me tell you, prospective tenants go "wow" when they tour the upstairs unit. Not so much downstairs.
If the trim is in good shape (i.e. not beat up), I would leave it. They don't make 'em like that anymore. Painted wood is a single tone. Stained wood has warmth, variation, and pattern.
Everybody is doing the monochrome thing. Just IMO - I'm not a fan. It's getting played out because so many rentals look the same. I think it's nearing its shelf life. I completely redid a unit last year in warm tones and I had cars parked down the street during the open showing. And this was in Maplewood. You don't need grey/white to attract tenants. Being in a historic district will probably be the draw, and prospective tenants might be looking for something with character instead of a cookie-cutter rental unit.
Choose paint colors that work with the trim, floors, cabinetry, etc. And you don't have to use a single paint color. I started using different colors in bathrooms, kitchens, bedrooms, hallways, etc. I want to attract a tenant that says "I love it!" rather than "yeah, it'll do."