in this case I think it depends how large an expanse of the kitchen floor is adjacent to the dark walnut floor.that could be tricky. If it's larger expanses,get the floor choice narrowed down as far as tile size/color/grout color/etc. Sure about a tile floor? the hardness can bother some people/others don't mind-it's cost effective certainly.

I don't know about the one "pop" rule, but you could do a dark walnut floor in the kitchen or a dark colored, wood look tile. The bianco antiqua is neutral colored, so you could add pop in the backsplash.

In my new kitchen, the range is the focal point, but if you face the opposite way, my fire place is the focal point. I have colonial gold granite, similiar colors to your your choice. I have ceramic, wood look, tile. It is a bit darker IRL and more contrasting to the cabinets than shown in this picture.

I should point out that I have decision fatigue and have no idea what kind of backsplash I will do, but I am leaning towards a neutral bs. I will add pops of color with accessories, upholstery and maybe window treatments.

Bianco Antico is a gorgeous stone, lots of color and bold movement so I applaud your instinct to choose a quiet bs. Here's an image of cream bevel edged subway tile slonewby used with her BA granite:

Another option, perhaps more modern looking, would be to use glass tile, either in subway format, or in a mosaic of sizes. This color is shell and would look great with your stone.

Are you open to the idea of changing the hue of your beige walls? Your color is a little over-saturated and will darken your space. If you love the color, keep the color, but I would go for something like Ralph Lauren paint in Petticoat White. I'm sure you can find something similar in BM paints.

RE: floors, one cool option you could choose would be to play off the parquet in the other rooms by choosing a basket weave pattern for your tile, as done so beautifully in the image below, designed by Newman and Wolen Designs in LA:

If you look closely you'll see dark and light grey rectangular tiles with one cream square tile. You can get this look with tiles that are a brown, grey and cream in a smaller format. Here's a board to show you what it all looks like together, shown with your BM wall color (note how much better it all looks with the bs covering your wall color).

I don't have many suggestions as i'm still stuck on what to do for a backsplash. I figured i'd share because I have the Ikea lidingo cabinets and had a hard time finding finished white ikea kitchen photos. I have a dark wood look tile on the floors, carrara countertop,and right now I think it's looking too white. Even though my floors pop, I'm looking for more subtle color in backsplash.

twn85 - you have so many options! Pick a color - almost any color. You can choose a bs with some brown hues so bring in the floor color a bit, stick to the greys but go mosaic with some green glass, or mix browns with your favorite color - mine's blue, and it works well with the greys in your marble. It's a lot tougher to pick the right bs with busy granites than with glorious marble. The possibilities are endless.