Get better protection on the floors ... even if you have to go in and do it yourself.

I would stain after cabinets. yes, my guys got a LITTLE stain on the cabinet bottoms, but it comes off pretty easily, and a good idea would be to painters tape it (my people didn't)...it's easier to do that than restain and fix the floor which can't be touched up in spots...

I'd install the floors first. Just protect them with builder's paper so they don't get scratched up. The cabinets sit right on top of the floor. This is for nail-down floors. If the floors are the floating kind (not nailed down), they need to be allowed to float so you don't want to stack cabinets on top of them.

Tina - given the expressed concerns about the condition of your floor and cracking, you may want to talk to your GC and/or Tile Guy about the deflection (the amount of bend/give) of your floor. If it has had wood and vinyl tile on it, it may not be able to support tile. To know this, you would need to know the type, size and spacing of your floor joists as well as the longest unsupported span. You'll also need to know the type and thickness of your subfloor. Floating will not help with deflection. The only things that would help are improving your joists and your subfloor. I went through this with our floor, unfortunately when it was too late to do the reconstruction needed. For me it worked out well, though, as we are winding up where I really wanted to be - with hardwood floors throughout our home. Here is a link that might be useful: Here's one calculator