Maybe or maybe not. Whites can be intermixed but you do have to see how they look together.

The easiest thing would be to repaint the wainscoting if need be.

im not sure I would limit myself when choosing cabinets.

.

It depends. You can sometimes successfully mix whites and creams. If your white wainscoting continues on trim throughout your house, I wouldn't change it in the kitchen. You may want to think about all the kitchen finishes. It might be better to use a white cabinet that coordinates with your wainscoting, and then use a creamy color on your countertops or back splash instead. Or possibly using the cream cabinets with a white back splash that matches your wainscoting. Post photos of your space, the color you are considering for the cabinets, and your other finishes in the room.