Start conservatively, then escalate the battle only if you really have to.
1. polishing compound; rub slowly by hand and with patience. Keep the abrasive on the streak as much as possible because it will cut the car's paint at roughly the same rate as it cuts the streak if the streak is also car paint.
2. rubbing compound, which is coarser; with even more patience.
3. abrasives of unknown coarseness, like toothpaste; if you are a gambler.
4. 600 grit wet-or-dry 3M sandpaper ONLY on the streak and only to thin it to save time with the polishing compound. DO NOT cut through to the car paint.
You can also try WD-40, which some consider to be the automotive equivalent of holy water. I don't know that it has every harmed paint but YMMV.
Solvents are dangerous and unlikely to work. Shopping cart bumpers are probably high density polyethylene, which is not soluble in even the nastier home solvents like acetone, MEK, etc. Normal car paint has polymerized into fancy molecules that are also not soluble in that kind of stuff. If you just can't resist trying a solvent "Goo Gone" is marketed as safe, but I would try it on an invisible section of car paint, like on the fender well lip. Put it on a white cloth and rub lightly, then check the cloth for car color. Wait a while and do the same thing again to the same area. Some solvents take a little time to soften paint, so you may not see color right away.