I've had hundreds of these intrusive thoughts. It helped me to know that the thoughts themselves aren't exclusive to anxiety. A lot of people have unpleasant thoughts pop into their mind but brush them off quicker than others.
Firstly not going on the internet helped, as did staying away from anything that might trigger me to have intrusive thoughts, such as alien conspiracies, etc. It doesn't help to read about other people's intrusive thoughts, for example, or research mental illnesses, because we have the kind of mind that takes everything on and doesn't let go. It's best not to give it any ideas. HONESTLY. Don't research it. You have an anxiety disorder and your anxious brain is going to take any rubbish you read and run away with it.
Secondly, psychology REALLY helped. You can't completely eliminate thoughts (and the more you TRY to stop thinking about it, naturally the more you think about it) No, you have to let the thought sit in your head and reduce the anxiety it causes you. Because the anxiety it causes is what makes us different to the average non-anxious person who has the same thought but doesn't dwell on it. Your "thats silly" response is the real you. The fear and worry that its actually real, is the anxious brain.
To reduce the anxiety, you need to sit with the thought and ride it out to the point of ridiculousness. Start thinking about aliens in a kitchen wearing an apron and hair rollers and making breakfast for humans. Start singing in your head (or out loud if you can) a little rhyme about aliens. Then say the thoughts aloud in your head in different accents (or again, say them out loud) these things should help to reduce the anxiety response so you won't feel so terrible.
Remember it's just a thought. Thoughts are not real. You can think about running through a shopping centre naked, it doesnt mean you'll do it. You can think about marrying some celebrity or going to mars... those thoughts are as real as any other thought... real ridiculous, that is.
Keep telling yourself "Is it realistic?" No.