I wouldn't do that, it's going to make them look dated & unprofessional. I'd paint the cabinets a soft white. It will help open up the space & keep the rooms looking fresh. If you're apprehensive about doing that because the counters are white, add some off white glaze to help add some contrast.

I think your bathroom would be perfectly gorgeous in shades of gray...take a look at the photos of this apartment in Manhattan from House Beautiful a month or two ago. I like rich color in bathrooms, myself...somehow it increases my sense of luxury, and of being safely enclosed and cushioned, while I'm taking care of myself. Here is a link that might be useful: NY apartment in shades of gray

How old is your house. If I get stuck I try to choose colors that would have been used when my house was built. Or you can go with those of a later remodel. For example I dont want an 1850's kitchen to match my house so Im pretending like it was remodeled in the 1920's. Still old but much more cook friendly. LOL. I see two ways to go with your bath. One would be to paint it a white that goes wth the tile. Then get your pops of color from your towels and accessories. Advantage would be easy redecorating. The other way would be to go with a contrasting color on the walls. You can go a little more crazy in a small room than you would in a large one. Lemon yellow, hot pink, cobalt blue, kelly green, cherry red, turquoise, apple green. If it were me I would use one of my accent colors from the adjacent room. That way it would go with the other room but not look like an extension.

my go to bathroom paint color is Behr Day Spa... it's a white with a hint of blue. It goes with anything, beige, white, anything. It would be a quick refresh with your existing tub/shower & floor. Are you replacing the vanity? I'd choose a simple white, but anything would work. I think replacing the outlet covers & switchplate, light fixture would be a fast fix and make you feel like you did an update without breaking the bank.