Instead of trying to match the peach or do more beige, I would try samples of warm whites maybe reading about which ones have the right undertones. That would pick up the white from sink and toilet & look bright with walnut cabinets. You’re not trying to match the porcelain- to me it’s okay for toilet etc to be standard stark white with warmer white elsewhere in a bathroom.
I don’t have specific named colors though. You will still want to try largish samples next to your tile.

Agree with finding a nice white for walls, then get a semigloss of same for trim and paint that cabinet white, if you need it.

Would you be up for wallpaper?

No, I'm not up for wallpaper.

I was thinking of a warm white, so at least I was going in the right direction. I really like the picture you ( lisedv) provided, just not sure how I feel about open shelves and having all our stuff visible. I do like the possibly of a white cabinet. I love how all the white really brighten up the bathroom. Thank you so much for the suggestions!

I would not go too warm with the white or it could end up in the yellow direction. I think you want to look for a white that has either a bit of peach or a bit of brown in it. Not enough to look like a color but enough to not actually clash with those two colors.

The brown tiles have a warm/red undertone. I suggest the walls be painted B.M. Franklin White.

Add art, with strong, correlating colors. Love to see it on the wall where the cabinet is.

Greatbigcanvas.com

waffle shower curtain: Target

Perhaps you can simply paint the cabinet the same colour as the white walls.

I do like the BM Simply White

Sarah, Simply White is a lovely white...I think it is too pale for the floor.

What about SW Alabaster?

I suggest you get the sample sheet for SW Alabaster or do a large sample sheet of it so you can see it in your space before you choose. If you go to SW hold a sample sheet of Pure White next to Alabaster so you can see the hue differences

Here are a couple ideas for beige and red bathrooms. i would try a creamy wall paint - for me white would be too stark, i would want to be on the warmer side. and then accessorize with color, like green, dark blue, or yellow.

https://retrorenovation.com/2016/08/23/decorate-beige-bathroom-1927-1962/

https://retrorenovation.com/2016/04/06/red-bathroom-colors-midcentury/

I am seeing a burgundy wall tile outlined in peach with a peach and brown floor. Is my screen color wrong about the dark maroon? Look at the second link in Stephanie’s post. At the bottom are the Readers’ bathrooms in deep maroon. That wallpaper in the first one makes the room! I have seen more of the peach main tile with the maroon trim, like in the other reader bathrooms. Today, we would never pair peach and maroon, but it was ”a thing” back then.

No, it is brown and peach.