If your studio lets you choose, this comes up eventually. Bare feet or grip socks. Both work. They just solve different problems.
What bare feet are better at
Direct sensation. Your skin reads the carriage, the mat and the footbar with nothing in between, and your toes can spread and articulate without any fabric limiting them. For slow, precise foot work and for anyone rehabbing a foot or ankle, that feedback is genuinely useful.
What grip socks are better at
Predictability. Skin grip changes as you warm up. Dry feet stick, damp feet slide, and the moment in between is where people lose a plank or a standing lunge. Silicone does not care whether you are five minutes or fifty minutes into class.
There is also the practical side. Shared equipment, shared floors, and warm studios. A sock is a layer between your feet and a reformer that fifteen other people used today. That is the reason most studios that require socks give.
Where socks lose
A badly fitting grip sock is worse than bare feet. If the sole slides against your foot, you get grip on the machine and slip inside the sock, which is the most unstable option of the three. This is a fit problem, not a sock problem, but it is worth naming.
How most people end up
Socks for reformer, tower and anything with standing work on a moving surface. Bare feet for mat work at home, and for the foot mobility drills where you want to feel your toes spread.
You do not have to pick a side. Keep a pair in your bag and decide by the class.