If you want to keep the tiles in the kitchen and you think beige will clash, then don't use beige. Use something with a bit of bluish green in it.

Blue green and tan will contrast and look choppy no matter what you do. It's better to have something be the same light/dark value but be a different color than to find something that's "close" but doesn't match. And even then, it will take some good design to make it look right. Most of the time it never will.

It's not that big a deal to tear out the kitchen tiles and retile so that all matches.

I am new to this site, but would like to chime on...

It is possible that hopper would like to have specific color schemes in certain rooms. There is always a way to blend any colors that you really love, but are afraid to place side by side.

Nature does it beautifully and gets away with it. But if you cannot find suitable inspiration there then look online at some of the mosaic trims available today. There appears to be one for every combination of hue and texture...

Check out 'Floor & Decor Outlets' and take a look at their random brick patterns of stick mosaic. One called Santiago Stick may be just what you are looking for. You can even combine a couple of products to include the closest match of shades to the beige and blue/green from your two adjoining rooms. Then place a border of these accent mosaic tiles around your new installation and I'm pretty sure you'll be happy with the result!

Good luck :)