Is it permissible in Islamic law to refrain from visiting a relative who drinks alcohol in his home, keeps a special refrigerator for it, and frequently mingles there with semi-naked women? And is it permissible to cut off this visit altogether?

Boycotting people of sins and innovations is a Sunnah for which one is rewarded, if the boycott is out of anger for Allah. It may become obligatory if it is the only means to reform the transgressor. However, if the outcome of the boycott is a greater corruption, then boycotting is not appropriate. Therefore, there is no harm in severing ties with a relative and boycotting them, hoping that they might desist from their transgression.