Here's the tricky thing about familial relationships, they're the first unintentional enablers of problematic behaviour and personality. So, I highly doubt that the letter that Shukla received from the family must have had any condemnation or reprimanding of all that he's said or done in the show so far. It gets worse in Asian families since the boys are mostly bought up with the 'raja beta' mentality and Shukla too has received a similar upbringing as far as I could tell.
Now, since most of these celebs leave their homes young, shift to different cities for work, a lot the habits, tendencies and behaviours they develop when transitioning from a young adult to adult is often in the absence of family or a familial protocol or construct that is in effect under parental guidance. So, I wouldn't be surprised that his family members are both unaware and inexperienced when it comes to Shukla's POS side.
I couldn't read a lot but when he held the letter up for a while, I could read something along the lines of, 'don't become the version that people want you to be (provocation)...'. Enough to gauge that his family too believe that he isn't wrong and is the one being provoked or instigated which is completely far from the truth. Like I said earlier on, most loved one's don't see their respective loved one has sides or versions of themselves that they'd never imagine in their worst of nightmares unless and until they have experienced it first hand.
Shukla's apology to Asim in that particular moment may be genuine but I don't trust him to change his ways for the good. At least not in the show. His bigger enablers, BB, the host, coworkers, friends or mentors from the industry, channel/production are there to serve him the trophy on a platter.