Always anchor heavy, tall or easy to climb furniture to a wall. Use either a stud or a drywall anchor. Even if you rent.
The holes are tiny and easy to spackle fill and could save your child, pet or elderly persons life.
Don’t be fucking lazy, anchor that dresser.
Drywall isn’t load bearing, though. Heavy also implies that it’s stable, although that really depends on if it’s top-heavy or bottom-heavy.
IOW, if my dresser is going to tip over, drywall anchors are not going to be doing much to stop it. Same for the couch, and the bed goes without saying.
It doesn’t need to be load-bearing because the actual forces aren’t that high. Fifty pound drywall anchors exist, after about fifty pounds the child will likely be old enough to not climb, and a fifty pound child’s angular force pulling out on the wall is going to be less than fifty pounds since most of the weight is going into the floor.
Certainly anchoring to the stud would be better, but drywall anchors are better than nothing and should probably be sufficient in most cases.
Why though? An ablebodied, childless adult without pets will very rarely ever have a random child or elderly people in their apartment.
The odds that you’d have someone at risk in your apartment, that you’d leave them unattended, and that they’d knock over an item of furniture is very long odds.