Should he shun those who slander and mock the scholars of Ahl as-Sunnah?

Firstly: 

With regard to reviling, slandering, mocking and making fun of (scholars), that is something that anyone could do. The most skilled of people in reviling and mocking are those who are furthest removed from religious commitment, good attitude and dignity. This is something that should not be done by one who understands religion; rather he should avoid it. The Prophet (blessings and peace of Allah be upon him) said: “Reviling a Muslim is evildoing and fighting him is kufr.” Agreed upon. 

Allah, may He be exalted, described the criminals and disbelievers in His Book, and listed as one of their attributes their mockery of the believers. Allah says (interpretation of the meaning):

“Verily! (During the worldly life) those who committed crimes used to laugh at those who believed.

30. And whenever they passed by them, used to wink one to another (in mockery);

31. And when they returned to their own people, they would return jesting;

32. And when they saw them, they said: ‘Verily! These have indeed gone astray!’

33. But they (disbelievers, sinners) had not been sent as watchers over them (the believers).

34. But this Day (the Day of Resurrection) those who believe will laugh at the disbelievers”

[al-Mutaffifeen 83:29-34]. 

So you should not worry about their mockery, for Allah will bring them to account and Allah will tell them what they used to do. 

What the person mentioned has to do, if he has knowledge and is religiously committed, and he has evidence to refute those who differ with him, is to quote his evidence and explain the truth he has, and leave slander and mockery to people of a lower status. 

Shaykh al-Islam Ibn Taymiyah (may Allah have mercy on him) said: 

Responding by merely reviling and shouting is something that anyone can do. If a person engages in a debate with the mushrikeen and the People of the Book, he should mention proof to highlight the truth he believes in and the falseness of their beliefs. Allah, may He be exalted, said (interpretation of the meaning):

“call to the way of your Lord with wisdom and goodly exhortation, and reason with them in the best manner possible”

[an-Nahl 16:125]

“And argue not with the people of the Scripture (Jews and Christians), unless it be in (a way) that is better”

[al-‘Ankaboot 29:46]. 

If a person is debating with one who uses foul language, even if he belongs to a group that is known for extreme bid ‘ah, such as the Raafidis, then all that he has to do is present his proof and avoid saying anything that is of no benefit.

End quote from Majmoo‘ al-Fataawa, 4/186-187 

Secondly: 

With regard to the ruling on shunning him and not greeting him or accepting his invitation, it should be noted that the basic principle is that it is haraam to shun a Muslim for more than three days, but that applies when the shunning has to do with personal or worldly matters. 

But if the shunning is for a religious purpose, such as shunning those who promote innovation or those who commit evil and immoral actions, then in these cases we should examine the Islamic purposes that may be served. If it is thought most likely that a shar‘i interest will be served by this shunning, such as making a follower of innovation give up his innovation, or make people disperse from around him, or reducing the numbers of those who are deceived by him, or weakening the spread of his innovation, and other shar‘i interests, then in that case shunning him is prescribed. 

Similarly, it is prescribed to shun those who follow innovation, especially those who open practise it or promote it, so as to protect people’s religious commitment from being affected by any of the specious arguments of the innovators or lest anything of what they say take root in his own heart, especially if he does not have sufficient knowledge to protect him against that. This is the principle that was followed by the righteous early generations. 

Al-Baghawi (may Allah have mercy on him) said: 

The Sahaabah, Taabi‘een and their followers, and the scholars of the Sunnah, followed this principle and were unanimously agreed on opposing and shunning the people of innovation.

End quote from Sharh as-Sunnah, 1/227 

See also the answer to questions no. 22872 and 47425.