Ever played Stellaris?

no, I haven't

The game is a grand strategy game set in space, and it let's you do some horrific stuff. It let's you set the rights of every species in your empire, and one of the options is "undesirables", which means they are going to be the victims of genocide. The game even let's you pick what method of genocide you prefer. There's extermination, where they are hunted down by extermination squads and presumably shot on the spot. Then there's forced labor, where they are worked to death. You can also turn them into food, energy if you're a machine intelligence, or paperclips, if you're that kind of machine intelligence. If you prefer a softer approach, you can forcibly sterilize them, so that they die out. Alternatively, you can displace them.

Imagine if alien life is common in the universe, but we are so ruthless and evil as a species compared to every other alien species they just don't want to have anything to do with us.

Issac Arthur is a fantastic YouTube channel that delves into the many possible types of alien civilizations and how they could fit into the Fermi-paradox (where is everybody?).

What you propose is generally not accepted as a likely state of the universe. If a civilization is ruthless, evil, and expanding the last thing a more powerful, peaceful civilization would want to do is allow its expansion. The logical choice would be intervention either in guiding their morality (probably hard), or just extermination (quite easy if you posses even modest interstellar space travel capability).

Fun to think about! We've only been broadcasting our existence for about 100 years, so it could be we've only recently been noticed and our doom is already en route!

But if a civilization is peaceful, would it exterminate another just because they are a threat? It seems quite ruthlessy egoistic. Maybe they would just intervene at some specific point, without extermination but by somehow gatekeeping our expansion and letting us live without spreading evil.

As even a type 1 civilization it costs you almost nothing to send a big ball of death a few million years into the future to wipe out a possible future rival.

The timescales are where things get tricky. If you wait for them to become a problem they will be a problem for millennia. and that problem will metastasize.

Now if you have FTL figured out. I mean. Carl from accounting could wipe out all life on earth because he had a bad day.