No, there aren't hard rules against it. Practically, however, it's not very useful to use a non-Windows OS depending on which team/product you're working with.
For instance, Macbooks are really common on some apps teams. In contrast, I work on the OS itself, so tools such as WinDBG and Hyper-V are essential to getting work done.
The kernel I start with is indeed derived from the same one that project started with.