How do I stop caring about what coworkers think?

Know your own personal Truth. You know you better then anyone else. What you're co-workers think isn't fact, it's based off of assumptions. Assumptions are dangerous, we are vicious when it come to what we assume about others, things we don't understand, or what is going to happen. Assumptions can be comforting because it's something we've created to fill the unknown void. In knowing your own Truth it leaves no space for doubt because all that matters is what you know to be Truthful. This can span beyond co-workers and apply to anyone in your life. Care about what you know to be Truthful about yourself.

Maybe you want to impress them and perform well. Maybe you want to form connections with them and you think you need to appear very competent and likable. Maybe the best way to find out what they actually think is to actually talk to them! Engage with them! Find out who they are, what they like to talk about. You´ll soon be able to form some connections with them and feel less anxious about what they might think. Good luck on your way .

Acknowledge that you were born alone, you will die alone and in between that is the time you have to leave a mark. Sometimes you can be wrong, but it's better regretting for your own opinion than for an influenced one. You miss 100 % of the shots you didn't make. You can atleast try your best, let them do their best. You always gonna learn from mistakes. Acknowledge your opinions, be the best version of you. The satisfaction you are going to get from it, will not let you care about others. Until you can't make it, fake it.