How can one deal with parents who constantly watch abominable things on television, while maintaining distance from them? Is it preferable to sit with them and condemn it in one's heart, or to continue to keep one's distance?

You should continue to advise your parents in the best possible manner. If they do not respond, then supplicate for their guidance often, be a good companion to them, and show them dutifulness by all possible means, bringing them good and warding off evil, while remembering that Allah is the Guide of hearts. It is obligatory to avoid sitting with them when hearing or witnessing evil. Denouncing with the heart necessitates leaving the place of evil, and the presence of guests does not permit remaining in this situation. If it is possible to convince them to turn off the TV or play something permissible, that is good; otherwise, act with wisdom to avoid embarrassment.