For cultural context, in case it's not clear why this question is interesting, Ertuğrul was portrayed in a 2010s television show Diriliş: Ertuğrul which became extremely famous throughout the Muslim world, including in Pakistan. The Indian Quora comment reads a Hindutva blog with false confidence in order to swipe at Muslims generally from a position of smug superiority.
As the Hindutva blog correctly reports, Ertuğrul is known only from coin inscriptions and from Ottoman mythology written hundreds of years later. The TV show Diriliş: Ertuğrul depicts this character and his tribe struggling for the cause of justice/Islam with other period tribes as a sort of late antique fantasy; of course Ertuğrul is chosen as protagonist since he is the ancestor of the Ottoman caliphate. It is retelling of old mythology, like an American frontier drama about Johnny Appleseed or Paul Bunyan or whatever.
Now the wacky stuff begins. The blog then reports on an Urdu book entitled "Daulat-e-Osmania" which goes further to say that Ertuğrul was a pagan. This book was published in 1939, and its source for this claim is some European Orientalist book which must be even older. It might be the 1916 Christian missionary book The Foundation of the Ottoman Empire which is excerpted in the Quora post, and which makes both the arguments of "Daulat-e-Osmania" while bemoaning the lack of Christian unity to convert the fickle Seljuks to their side.
Anyway, this Orientalist source makes two confused arguments. The first is that Ertuğrul's father was "Suleyman Shah", whom the Orientalist claims was pagan because he was descended from Turkish pagans. But Suleyman Shah (a strange name for a pagan anyway) is known to historians only as a legendary character from Ottoman hagiography, so we cannot have that level of confidence about his religious practice. The second is that "foreign travelers" in the 13th century did not find any Muslims in Turkey. But no foreign traveler claimed to meet with Ertuğrul, whose name we know only from coins, and it is not known what Ertuğrul's tribe was; his connection to the Kayı tribe claimed by Ottoman historians has been strongly doubted as part of a manufacture of legitimacy for the caliphate.
We do not have any evidence that Ertuğrul was either pagan or Muslim. He is only a name on a few coins. The historical consensus is best expressed by the recent book Osman's Dream:
Beyond the likelihood that the first Ottoman sultan was a historical figure, a Turcoman Muslim marcher-lord of the Byzantine frontier in north-west Anatolia whose father may have been called Ertuğrul, there is little other biographical information about Osman.