I'm having a hard time putting it in perspective

modern white would be a nice contrast to the rustic of the tile.
if you want to juxtapose those two looks, i would say any clean-lined cabinet would work, no matter the color.

Little bit more crisper I'm liking this look a little better

Gray perimeter cabinets and graphite type stain for an island.

This is the house it's going in

Blueprint

White will go...but to make the cabinets as special as the floor...why not do a taupey gray...complimenting the gray colors that are in the floor....especially for modern. However; if you can afford to ...I would make the cabinets custom and in alder...then if you get tired of them or if you sell the house...anyone could come in and stain them and still keep the floor and do almost any wood finish making the kitchen in virtually any style.

Great contemporary house. I'd match my countertops to the gray in the floor, and use waterfall edges to echo the box facade. Instead of white cabinets, consider blond wood and mix in charcoal or black depending on your window frame colors . . . even a shot of cedar like these . . that will bring out all the tones in that gorgeous floor .. (and itis a candice olson trick to match counters to floors - horizontal planes that echo bring harmony)
[houzz=]

Like this?

I would like the grey and white shiny cabinets against that weathered-looking floor, which would let you mix strictly modern (like the house) with a few other rustic touches if you wanted to (like oil-rubbed or iron bits)...

here is a smattering of examples that might help you refine your preferences...

That looks like the porcelain tile I'm planning on installing, rustic bay, and I am going with painted linen beadboard type cabinets, a Quartz countertop with brown/gray and black fleks, and a distressed walnut butcher block on my island...any thoughts if this all works together? I'm new at this...

Love the butcherblock . .. think you may want quieter quartz - make sure the undertones of the browns work - what you posted . . not so much. . . floor cool brown, quartz warm brown . .

I guess this helps me as well since I'm looking to lay the same color floors. I like the grey cabinets. looks fine!

I would do greige (grey and beige). Look at habersham homes