Great question. I've always done a medium or light stain, but haven't noticed any issues with dirt showing in the cracks. I may have just enough color to camouflage it though.

I too love the look of those Scandinavian floors and think you should embrace it. I suspect it is in the shorter run that you may notice the space between the planks darkening just a bit. In the long run all the spaces between the planks will be just a bit wider and darker and look consistent. This, at least, is the case with our 90 year old white oak floors (though our stain isn't as light as you are contemplating). If I were you I'd go with the very light natural stain on white oak (not pickled, as that may go out of fashion more rapidly). White oak is extremely durable, and if you don't like how they look in 10 or 15 years, you can always refinish them a bit darker.
P.S. I LOVE Bernese Mountain dogs. Lucky you.

Take a look at www.lvwood.com. There are some beautiful white hardwoods on that site. Dirt between the planks? I am sure with kids and that fabulous breed of dog you have the vacuum is out often enough to deal with that issue. Go for it!

Floors finished on site should have minimal cracks or crevices for dirt to collect in. That being said, white or light floors will always show soil faster or need to be cleaned more frequently. Another consideration is the resale-ability of your house. Even though you love the look, most buyers run screaming from a house with white floors.

We just finished up a house with a clear finished maple floor in the kitchen, against white cabinets and dark countertops. Yes, it does show spots and dirt faster than the med-dark stained oak. The comment about site finished floors is a good point, prefinished has bevels on the edges of the pieces which naturally create channels for dirt to accumulate. You can actually save a bit of money on installation by eliminating the stain step and then, using a good waterborne finish, you can get three coats of finish on the floor in a single long day