Anxiety has a function. Appendix does not and it's because of another evolutionary success.

My therapist has took this angle immediately - anxiety is a part of us and has a real function - to make us more cautious. But in the modern world it misfires and makes us anxious about things we don't need to be anxious about which can stop us from doing what we want/need to do. So you acknowledge that voice within yourself, understand that it's coming from a good place, and then gently push it aside.

I mean I suck at actually doing this but it seems like sound advice.