Classic example is Kirk going into their new more sophisticated warp chamber with no radiation suit and kicking it to fix it allowing them to do a last minute 180 degrees in an atmosphere (but having just watched Dagger of the Mind - it's not much sillier than Helen crawling through the air conditioning to flip a switch to turn off the power in a high security hospital I guess...).
Classic example is Captain Spock having to go down to Engineering to fix the mains, wearing no radiation suit when they have twenty guys standing around already in partial radiation gear.
I could see someone who had just saw the latest movie and had no other exposure to Trek criticizing these things. But for long-term Trek fans, non-sense is the status quo and it seems kind of funny to be complaining about it now.
No, I've always thought it odd that engineers didn't have helmets for their radiation suits but I suppose from a cinematic perspective you want to see the actors' faces but at least the partial suits look better than the no suits of TNG through to NuTrek. Even TOS tended just to wear overalls.
However, my understanding of TWoK was that even with radiation suits on, a human would lose motor control too quickly to be any use (robotic drones anyone?) whereas Spock, even without a suit, believed he could do the task (not to mention that the decent engineer had just fallen unconscious and the others were inexperienced cadets).
That's a bit diffeent to NuTrek where there are not even any engineers (trainees or otherwise with or without suits) in the key affected section of the ship and the human goes in to kick the ship back into order with no suit.
They're both a bit silly, yes, but they are not qualitatively the same. TWoK did have some plausible excuses to frame the scene, NuTrek less so IMO. Not that there were not a number of other REALLY silly other moments in TWoK.