SRAM officially endorses cross-chaining. Shimano doesn't, but their drivetrains appear to tolerate it, at least in my experience. Recent iterations of Di2 prevent you from doing it.
SRAM has been the main proponent of 1X gearing (probably because they can't seem to make a functional front derailleur). I got curious about this, because the same arguments that apply to cross-chaining should apply to 1X, at least for the lowest gear, so I checked their website, and found that out, so at least they get points for consistency.