May Allaah love you, for Whose sake you love us, and may He bring us together in His mercy on the Day whereon neither wealth nor sons will avail, except him who brings to Allaah a clean heart (al-Shu’ara’ 26:89).   

With regard to what you have said in your question, we advise you to keep away from everyone who speaks about your Muslim brothers or slanders them, or accuses them and casts aspersion on their intentions. The Prophet (peace and blessings of Allaah be upon him) said: “O you who have spoken the words of faith but faith has not entered your hearts! Do not backbite about the Muslims or seek out their faults, for whoever seeks out their faults, Allaah will seek out his faults even if he is his house.” Narrated by Abu Dawood, no. 4880; classed as saheeh (authentic) by al-Albaani. 

It is also necessary for you to advise these people to fear Allaah and refrain from using such labels and names that divide the Muslims. With regard to offering advice and correcting mistakes, this should not be done by means of exposing people’s faults or casting aspersions on their intentions etc. 

With regard to the issue of takfeer (labeling people as kaafirs - non-Muslims), this is subject to further discussion. Describing as a kaafir one who has been described as such by Allaah or by His Messenger (peace and blessings of Allaah be upon him) is obligatory. Allaah has described some groups as being kaafirs in His Book, as when He says (interpretation of the meaning): 

“Surely, disbelievers are those who said: ‘Allaah is the third of the three (in a Trinity)’”

[al-Maa’idah 5:73] 

“Surely, in disbelief are they who say that Allaah is the Messiah, son of Maryam (Mary)”

[al-Maa'idah 5:17]

But it is haraam (impermissible) to label as a kaafir someone whom Allaah and His Messenger (peace and blessings of Allaah be upon him) did not label as such. 

Shaykh Ibn ‘Uthaymeen (may Allaah have mercy on him) said: Just as it is not permissible to label a specific person as a kaafir unless the conditions of labeling someone as such have been met in his case, so too we should not shy away from labeling as kaafirs those whom Allaah and His Messenger (peace and blessings of Allaah be upon him) have labeled as such. But we must differentiate between what is specific and what is general. 

Sharh Kitaab al-Tawheed, 2/281. 

See also question no. 21576. 

And Allaah knows best. 

Moreover, everyone who levels an accusation against another person must provide proof: 

“Say (O Muhammad), Produce your proof if you are truthful”

[al-Baqarah 2:111] 

“Since they produce not witnesses, they are the liars in the sight of Allaah”

[al-Noor 24:13]

This problem is widespread among some of those who claim to be religiously-guided, may Allaah guide them, for they make accusations against people on grounds that are not regarded as something worthy of criticism in sharee’ah or that do not undermine a person’s religious commitment.  

Then they do not bring any proof of that, and they follow their own whims and desires, because it is human nature to appoint oneself as judge, praising and condemning on a whim.   

We must go against the whims and desires of our own selves and measure people by the criteria set out in Islam; we should make mention of their good points and advise them with regard to their mistakes. 

And Allaah is the Source of strength.