They probably had a spell or potion wich made them invisible to muggles

Hermione has mentioned about “Hogwarts a History“ that there are all the enchantments under the sun on Hogwarts so when they are in here it looks like a bunch of old ruins

I mean, I really doubt most Muggles would see it and immediately assume that it’s magic? If I saw a guy shooting magic light beams out of a stick, I think I’d just assume that they had a fancy laser and move on with my day, and I’d probably just assume that I ate or drank something weird if I saw a magical creature.

Great question ❤️

They called it a war, but it wasn’t really a traditional war. Mostly, it was just a (mostly) bloodless coup. There was a single battle, in a place that is invisible to muggles. Other than that, the Death Eaters just took over the ministry with little difficulty and started implementing their own evil policies. There was very little for the muggles to see.

Most of the fighting happed at Hogwarts and if there were other places the minister of Britain just made something up to cover what really happened

There were no muggles in the inhabitants of nearby places from Hogwarts. As the castle was under enchantments that would make it look like ruins, no ever came near it. The nearest village was Hogsmeade and it was magical too.

There are enchantments that stop muggles seeing it

#hogwarts a history