Is it safe to unplug an extra monitor from a laptop without turning off the monitor?

I have an extra monitor which is connected to my MacBook Pro 13 2020 using a USB-C to VGA convertor. Is it safe to unplug the extra screen without turning off the monitor? Because when I plugged in the charger, the extra monitor turned off for two seconds.

Best practice is to always power off any devices that are not designed to be hot-pluggable before disconnecting them. VGA is not hot-pluggable, therefore its cables are not designed to be disconnected while powered.

That being said, in reality, it is perfectly safe. While you don’t see VGA being used much these days, it was far more common 15-20+ years ago. I have physically disconnected and reconnected hundreds of live VGA connections with not a single issue.

Some monitors might have problems with incorrect timing. (I don't want to describe how CRT and LCD monitors work, etc. See Wikipedia pages or OSDev for that.)

Some monitors, both CRT and LCD, according to OSDev Wiki page (the big bold red warning at the top of the page) can have problems with wrong timing information and disconnecting the VGA connector can make some pins to lose connection before others and that could possibly even damage the monitor.

Well, it is quite safe (at least for newer monitors), and, if you need to do that, disconnect the monitor. All LCD monitors I've used do support hot plug, or, at least, work well when they are disconnected while running. I've seen (and “repaired”) monitor that was fed using connector with dirty horizontal sync pin. It was displaying funny pictures, but it did not get damaged.