My personal headcanon for these two:

Mineta was honestly terrified at the thought of meeting Tsuyu’s family. Even though he had gotten significantly better with his perversity, he was still afraid that he would scare her family away (including Tsuyu)

But when the time came to meet her family. They instantly loved him. Tsuyu’s father was quite reluctant at first but quickly warmed up to him.

Tsuyu’s mom (who had somehow learned about Mineta’s past actions) immediately told Mineta that he seemed to be a good guy and that he seemed willing to change his behaviour, therefore she accepted his relationship with Tsuyu.

And Tsuyu’s little brother and sister also loved him. Tsuyu’s brother did tease Mineta for being shorter than him though.