My uncle who is clean shaven is extremely annoyed with me because I neither offer Salaam to him nor respond to his Salaam.

Answer

Rasulullah (Sallallahu alayhi wasallam) said: ―When a faasiq is praised (honoured), the Arsh (Throne) of Allah shudders (in disgust).‖

A man who shaves his beard is a faasiq of the worst order. He flagrantly advertises his fisq. His flagrant act of blatant disobedience is perpetual. Every second of the day, the la'nat (curse) of Allah settles on him. He is utterly shameless. His perfidy borders on kufr. His blithe disregard for the Command of Allah Ta'ala is a stunning act of gargantuan hypocrisy.

Such a faasiq has no shame for Allah Ta'ala, for the Malaaikah and for Muslims. Thus, your uncle should direct his annoyance to himself. He should meditate on his extremely abhorrent act of kufr the kufr of rebelling against Allah Ta'ala in a similar way as shaitaan had rebelled. The clean shaved face of a man resembles the smooth skin of the carcass of a skinned pig.

The Masnoon Salaam is an invocation of the mercy of Allah Ta'ala. Therefore it is an act of rebellion against Allah Ta'ala to invoke His Mercy on a man on whom Allah Ta'ala showers His La'nat (Curse). It is like reciting the Tasmiyah when eating pork and drinking wine.

Your act of refraining from Salaam for your uncle is valid and incumbent. Ignore his umbrage and anger. Without disputing with him, be firm on the Shariah.