If you kept the lids off of 2 sourdough starters, side by side, that MIGHT cause me to worry about cross "contamination." But, an idy dough next door to a starter is nothin'. Apples and oranges.
BTW, I don't think it hurts but I do not see it to be a big deal to put a good lid on the starter. I have 4 in my beverage fridge side by side with lids on for a year now. But, I would probably get a little concerned if the lids were loose. The starter in the fridge lives just fine with a lid on it.