It means people are not happy about something for some reason and they are directing their negativity at you unjustly and/or wrongly. They are unhappy about their insecurities in this case.
to take it/something out on someone - to unfairly, wrongly, unjustly direct negative emotions at one person or a group of people. Many times it is anger, though not always.
ANGELA :"I am so sick of people taking their insecurities out on me. "
I am so sick of people directing their negative emotions and thoughts at me due to their insecurities. It is not my fault that they are insecure.