Not sure if I am understanding that you wish to keep the red wall and white wall behind the cabinets is this correct? In any case, I think you should get paint sample chips that pull directly from the various colours you have going on in your floor (there seems to be several different tones there). Then narrow it down to the top three or four you like and pick one of those for your cabinets. If you like darker overall feel in your room, go with a darker tone, lighter feel, a lighter tone. I assume it would be alot of work to strip it and use a wood varnish if there is a nice wood under the white paint of those cabinets and if so, painting is an easy solution. I hope we get to see a before and after!

Beautiful room. Are you keeping the curtains? If so, show a couple photos. A silver blue in a lighter shade of the curtain blue for the walls might be a new look without painting the cabinets dark.

Priming the walls for new paint will take several coats. It is easiest to choose a new paint color once the very dominant red is no longer there.

I think green would look fabulous.

Take a look at some of these beauties:

https://blog.scoutandnimble.com/blog/green-paint-colors-inspiration-blog

I’m not sure the tone of green you’d like, but here are some ideas:

Love this Benjamin Moore Peale Green:

And BM Essex Green, glossy, beautiful:

Farrow & Ball Carriage Green:

https://www.farrow-ball.com/en-us/archived-paint/carriage-green

F & B Studio Green:

Sherwin Williams Secret Garden:

Others for inspiration: https://www.farrow-ball.com/green-paint

Are you planning a rug? I think one would look nice with the lovely style of traditional furniture you have.

This is a lighter olive green built-in, but wanted to show the rug:

I have no idea what happened with that comment!

I've got zero color suggestions, but wanted to say I absolutely love your dining room furniture - it's stunning! If anyone tells you to change it, please ignore them (that goes triple for the inevitable folks who encourage you to paint that gorgeous hutch)!

Because your look is very traditional, I'm accustomed to seeing the built-in's painted in the same shade as the trim (but that doesn't mean you have to do that - just what I've seen in most traditional rooms).

I don't think changing the color of the built-in cabinets will do much for the room. A better way to go, IMO, would be to add a gorgeous rug (36-42" larger than the table top all around,) change the drapes (that buffalo style oversized check is not a formal look that goes with the style of your room,) change the chair upholstery and get a chandeiier that adds more pizazz. Here's a look to inspire you.

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If you’re really wanting to change the walls to white consider getting it all primed first to see the idea of it. Are other rooms nearby also white? For the cabinetry I love the blue sheen color on your dining chairs, maybe something that ties into that. Lovely space as is!

I second Maureen's suggestions, and strongly suggest you keep the cabinets white.

Another day on Houzz!

.

(I’m just teasing, all.) :D

Are you wanting to keep the red? If so it might work best to paint them a light cream color. Doing a black or dark green might end up making the room feel small and dark. If, however you are open to repainting the red, you might be able to add some blue to the area like you see below in a few of our designs:

Luxe Living in Zionsville · More Info

Luxe Living in Zionsville · More Info

Country Estate Transformation: Home Bar · More Info

Urban-Modern Centerville Farmhouse · More Info

The OP said the walls would be changed to white.

Would love an update.