How should a son deal with his father who mocks the beard and the short thobe, and is it permissible to greet him and wish him well, whether this father or anyone else who commits such an act?

If the mocker's intention in ridiculing the beard is to mock the religion itself, then it is apostasy and disbelief, based on the Almighty's saying: "Say, 'Is it in Allah and His verses and His Messenger that you were mocking?' Make no excuse; you have disbelieved after your belief." However, if the mockery is directed at the bearded person for other reasons, such as him being considered rigid or the like, and the intention is not to mock the religion, then it is not disbelief. Rather, it is a reprehensible and dangerous act. This person should be invited and advised by explaining the seriousness of his action.