The main issue seems to be that (a) they need full time childcare during the workday period, regardless of whether they are home or not, and (b) the childcare cannot take place inside the same house where they are working.
The opinion I’ve heard most is that if it was non-pandemic times, at best they would be indifferent or maybe commute would be the factor, because the kids would be going to stay somewhere via family / day care / school.
But in the case that kids have to be home because school is shut down / child care closes / child care has to be hosted in the same place where they are working, it’s a straight up no-go, 100% dead set against it. The employer must provide some different pandemic-acceptable option, like private offices that don’t require mass transit to get to.
It has been almost completely one-sided in our surveys and company all hands meetings, all parents with school-age kids or younger are completely against remote work (this is maybe 200-300 staff), and everyone else is completely against anything other than remote work (around 700 staff).
Full disclosure: I am one of the 700 with no kids who prefers switching to 100% remote.