All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah and that Muhammad is His slave and Messenger.
When a person is proven to be a follower of sinful inclinations and a caller towards deviated ideas with certainty, then it is lawful to warn people against him; rather, it is obligatory to do so in abidance with the obligation of offering advice to others that Islam enjoins upon Muslims. It was narrated on the authority of Abu Saʻeed Al-Khudri that the Prophet said, "He who amongst you sees an evil deed should change it with his hand; and if he cannot, then with his tongue, and if he cannot, then with his heart (by rejecting it in his heart), and that is the least form of faith." [Muslim]
The scholars excluded warning people from advocates of falsehood from the prohibited backbiting. Al-Haytami wrote:
"In principle, backbiting is prohibited; and it may be obligatory or allowed in certain cases for a valid purpose that cannot be realized except by it. (He then listed the cases in which backbiting is allowed) ... The fourth is warning the Muslims against evil and giving them advice, such as mentioning the flaws of weak narrators of hadeeth, unreliable witnesses (in court), and scholars who issue fataawa or teach Quran while they are unqualified for it or those who commit immoral acts or religious innovations and call others to them, even if they do that secretly. This (warning people against all those) is permissible by scholarly consensus, or, rather, obligatory. It also includes pointing out the flaws, even if one was not consulted, of a person who proposes for marriage or who wishes to mix with others for religious or worldly affairs if one knows that that person has a flaw that is ugly and repulsive such as immorality or religious innovations or greed, or other flaws like the poverty of the suitor proposing to marry... The fifth is if a person is openly committing immoral deeds or following religious innovations such as drinking wine, confiscating people’s property unlawfully, collecting extortionate taxes, exercising unlawful authorities, etc. It is permissible to speak of what he is doing openly, but it is not permissible to speak of other flaws except for another reason..." [Az-Zawaajir fi Iqtiraaf Al-Kabaa'ir]
It is also prescribed to warn non-Muslims about harm as long as it brings about sharee'ah-acceptable benefits. Al-Haafith Ibn Hajar, may Allaah mercy upon him, wrote, "Offering advice is mostly restricted to one's fellow Muslims; however, offering advice to the non-Muslim is acceptable as well, such as in the case of inviting him to Islam and offering him correct direction if he consulted the Muslim." [Fat-h Al-Baari]
Indeed, the deviated ideas of a person such as the one that you mentioned distort the image of Islam, contrary to what is required, which is encouraging people to embrace Islam.
Lastly, we would like to emphasize that the Muslims are enjoined to verify the accusations and not to hasten to label one's fellow Muslims as religious innovators without strong evidence. It is better to resort to the knowledgeable scholars endowed with piety and righteousness in this regard. Taking this matter lightly is quite dangerous and may lead to falsely accusing an innocent person of what he did not do; verily, this is a grave evil. Allaah, The Exalted, says (what means): {And those who harm believing men and believing women for (something) other than what they have earned have certainly born upon themselves a slander and manifest sin.} [Quran 33:58]
Allaah knows best.