The mas'alah is that a faasiq should not be offered Salaam.

Answer

Understand well that allegiance and obedience are first to Allah Ta'ala. It is haraam to obey even parents in anything which is in violation of the Shariah. The Qur'aan and Hadith are explicit in this prohibition.

Your father despite being a flagrant faasiq has to be respected by you. However, such respect has to incumbently be within the limits of the Shariah. If you are certain of a danger for your father in some deal or activity - that he will suffer monetary loss or sustain bodily injury from the danger, what will you do? Will you remain a silent observer of the harm and calamity befalling him? Obviously not. You will alert him and do whatever is possible to prevent him suffering harm.

What harm and danger are greater for a Muslim than the calamity of Allah's Wrath and the Athaab of Jahannam? However, since belief in these transcendental truths and realities is extremely deficient in most Muslims, in fact their attitude demonstrates lack of belief in the Aakhirat, they do not view the calamities of the Aakhirat to have any significance, hence they are silent in this respect.

If your belief in the Aakhirat and its calamities is real and alive, then you will act in the best interests of your father to save him from the Athaab of Jahannam and the Ghadhb of Allah Ta'ala. You have to offer Naseehat to your father. You have to explain the Shariah's stance to him, and to very respectfully explain to him that the Shariah has tied your hands and does not permit you to offer Salaam to him nor may you respond to his Salaam.

In so doing, you will be acting in his best interests and will be motivated by concern and love for him. Obviously, the faasiq will not understand this stance. He will rebuke and revile you. Maintain silence and do not lose respect. But remain firm on the Shariah.