How do I deal with neurotic colleagues who project onto me all the damn time and act accordingly? They keep trying to find me flaws?

I have started this new job as an intern and I need my colleagues/ supervisors's blessing to definitely get the job and these people are a nightmare.

My supervisor projects her insecurities into what she interprets. Her and others want me to be for instance: insecure, ashamed, with an illness, mentally disabled etc etc. They keep moving the goalpost to try and find me flaws whenever I prove them wrong. My supervisor also hacked into my google account and takes for granted stuff I wrote years ago and keeps reiterating these things to me (I realize this by rereading it).

These women are midle-aged and yentas and low-achievers by the way.

How do I mentally accept that they will keep on trying to downgrade me to their level? It makes me upset and I do my best not to play nice but I cannot avoid them.

They also downgrade my work, one of them made comments about my online research and downgraded it, she was clearly bothered. Another one convinces herself I did not go to the uni I went to but was in a special program.

They cannot accept they did not do their best in their own prime time.

My tactic is to avoid and ignore but it is mentally draining since they are the ones who will give me the job. Should I play into their fantasy to secure the job? I am really fed up and need to wait maybe 8 more months.

How do I deal with neurotic colleagues who project onto me all the damn time and act accordingly? They keep trying to find me flaws?
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