50 years ago the terms 'port' and 'starboard' were still used. I recall textbooks referring to both in the sections on lights and right of way. Nautical terms such as 'abeam', 'aft' and 'locker' may still be found in some manuals. Fokker certainly used those terms in the English versions of original F27 literature. The neat thing about nautical terminology is it leaves less room for misunderstanding in a noisy environment.
As for the current debate, why stress over a simple word? Whether ''SIDE" is included or not, it won't make a blind bit of difference if you don't actually look outside first! A bit like whether you parrot "xxxxx checkLIST complete" or "xxxxx checkS complete" - it means nothing if you haven't done it properly.
I will endeavour to use whatever my paymasters require, although I sometimes forget the exact fly-by-mouth words, especially if there are too many of them required to describe something basic. I see no safety hazard in an occasional lapse if the meaning is clear, unless the other guy in the cockpit is either a moron or so hung up on having the exact words that he goes into a catatonic state when he doesn't hear them.
It is when pilots rebel against SOP just to be different that a hazardous attitude can develop.