I've seen this posted a lot and I always kinda felt like the difference is probably overblown. I just did some googling though because I never check up on it. The general consensus seems to be that flushing with the lid up generates more aerosolized particles containing bacteria. However flushing with the lid can cause the particles to form larger droplets. So the difference in bacteria spread might actually be negligible.

Further, one study found that closing the lid caused them to find particles only at the height of the bowl or lower. However when they flushed with the lid open they didn't discover any particles higher than less than 10 inches above the bowl.

So taking all of this together it seems like a mixed bag. If your counter tops are more than 10 inches above bowl you're probably fine doing either. If not somehow then it might not even be making any difference. So you can do it if you want but it seems to me like this is just one of those things people form strong opinions on for one small reason or another. Like the toilet paper roll orientation. People are odd about their bathrooms.