I can think of many things that might have the properties of a reasonable tribological agent for intimate purposes, but toothpaste doesn't leap to the top of that list. I'd probably advise against, and not from personal experience, Swarfega. Growing up, we had tubs of that everywhere, mostly because my mother's brother-in-law worked in the factory and kept bringing it home.
That said: boys. I went to school with a young man who abused himself regularly with an Atari joystick. Everyone who'd been around his house to play Pitfall before that reveal had cause to need a lot of Swarfega. I was scrubbing for weeks. There was another guy who apparently liked to splash out on cacti. I have no idea. I like botany. I don't like it that much.
A friend and I once ate a tube of toothpaste in an attempt to hide the smell of Woodpecker. It didn't work, we just foamed at the mouth like we had rabies, and we smelled like minty sick.