if you don't, then no I definitely wouldn't put that in the communal fridge. But if part of the worry is the food "taking on" smells/tastes of other foods, wouldn't that happen in the bag if it's not in any other container? I guess if you bring a sandwich every day then no, it wouldn't, but otherwise (like me) it's different foods each day and I don't want those smells mixing.
And if there's plenty of room, yeah who cares. No worries. I personally don't think the insulating thing in the fridge matters. But I have not been so lucky with lots of fridge space and still see it happening. Sorry if it takes an extra 10 seconds, but can you share the limited fridge space? This is not a picture of me (source: Reddit) and is a bit of an exaggeration but sometimes this is how I've felt:
https://www.reddit.com/r/funny/comments/8si4cw/what_its_like_working_with_all_women_and_their/