When my Dad, in 2019, accused me of lieing (making it up) about what was happening to my sister and her children, it made me sink into a depression and spurred me on to tackle my past and start therapy. It was incredibly hurtful to me that he accused me of that. For so many reasons: that he was denying the hurt his other child and grandchildren were going through, that he wasn't going to do anything to help protect them, that he preferred to think I was a manipulative person to make up such lies (the situation was really bad: brother in law had tried to strangle his 15 year old son and my sister: something that could have been fatal, police and child services were involved, thankfully), and it reminded me of my past and how he failed me then, and that failure was repeating now.
How did I process that? It was tough. Long. Therapy. Distancing myself from dad. Working through the hurt. Difficult. My relationship with him and my mum, and my family, changed significantly following all of this. It was the final straw in some ways of the pain of my family and their denial of reality.
Another example. Last week at work, a peer said I was offensive to her because I said what she was asking from me was to change things to support her and it didn't help me do my work. Which was true. She took it personally. But she wanted me to change something, that is a company way of doing something and not mine, because she is struggling with managing her diary. She was offended because it was a sensitive issue for her. I didn't apologise because I had nothing to apologise for. I didn't feel guilty about her accusation. I was worried she would make a complaint about me as I don't trust her. But, I have been able to be boundaired about it and get on with my stuff. This is a her issue not a me issue so I am leaving the issue with her. Not soaking it up.
Like @alfie says, context is everything. Those two examples show how difficult it can be if the accusations runs deep and is by someone who means a lot. And the second one shows how easy the accusation is to deal with if it is by someone not close and you're clearly it's not a reflection of you or a repeat of a deep occuring issue.
Do you want to share the context?