Absolutely not.
Solid-soled shoes - ones that don't squish down or bend side to side - are very important for giving you a stable base of support that enables productive training. They make things far more efficient because they prevent wasting force, enable better balance, and allow each rep to be more precise. It's like bare feet to wearing flippers while swimming.
Your question gets things inverted: it's at low weights relative to a person's strength and facility with a movement pattern where shoes are less important. New lifters, lifters with any kind of balance/coordination deficits, lifters who are training - and thus pushing in to their abilities - are among those who benefit most. IOW, it's the strong guy with plenty of experience who cruises right along with light-medium work while wearing running shoes and no belt during the quick workout he gets in while traveling with his family.
Don't handicap your training with poor equipment.