Who is Baphomet?
According to some, Baphomet is a demon, worshipped in Theistic Satanism. This may now (since 1854) be the case, (but this was certainly not the case during the time of the Templars) It has not always been the meaning of the name, the origin of the word might quite surprice you.
The simple truth behind the name.
Baphomet is nothing more then a french misspelling of the name mohammad, the inventor of islam. (*) According to the "trails of the templars" Not so misterious now is it? Ofcourse this name would have gotten up many times during their trail, since Templars were the arch enemies of islam. It was the intend of the inquisition to link the Templars with idolatry and pagan worship. Claiming that their association with pagan mohamedans in the holyland had corrupted their holy faith in Jesvs Christ the Son of GOD and that the Templar had turned islamite. This was important in tying the knot in the process against them, and "proving" that the templars had become infidels, heretics and practiced idolatry and sodomy like the Saracenes (+).
The belief that templars were demon worshippers, was introduced by king filip of France, to discredit the templars and has ever since been the "standard" history about Templars.
We understand that the human mind likes and seeks mysteries, but most of the time a simple/boring fact is at the root of it. However over time things get blown out of proportion or out of perspective, that is when mysteries and legends are born. Ofcourse later in time this name (Baphomet) may have gotten associated with/adopted by, Satan worship for which the image see here on the left is responcible. 
Here is what the book "The Templar code for dummies" says: "What Baphomet doesn't seem to have meant is what it has come to represent in modren times: the image of the winged, goat-headed, cloven-hoofed demon that commonly appears on tarot cards. Nineteenth-century French mystic Eliphas Leví came up with the drawing for his book "Dogme at Ritual de la haute Magie" in 1854. Although Leví "claimed" Templar origins of his mystical figure, testimony from the trials of the templars, describe no such thing." (**)
More over, if freemasons belief and worship Baphomet, the goat. This does not mean Templars did! Templars never worshiped any other then GOD and His son, Jesvs Christ.
(*) we use the term inventor here, because to us, the Templar Church, and to any other true Christians, this man was not an inspired prophet of God, because Jesvs was the last messenger send by God to mankind. This puts mohammad in the same group as ron l. hubbert who invented scientology and joseph smith, who invented the mormon church. see True Prophets
(+) Saracenes, medieval term for describing all arabian tribes and nomadic tribes of the dessert, all that follow the mohamedan cult.
(**) The Templar Code for Dummies - part 2, chapter 6, page 147, last paragraph.
The Bearded Head
Was not according to some accusations, one, where the templars supposedly possed some kind of demon head?
According to some scolars, the templars might have had in their possession a scul or mummified head (belonging to John the Baptist). However nothing according to reccords of the trails proof they had such an head or scull, found, among the items belonging to the templars. (The bible even states that herodias recieved the head of John the baptist [Matt 14:8, Marc 6:25] And nowhere does it say she gave the head back to his disciples.)
But even if they did have such a bearded head, would this make them demon worshippers? No, Templars lived in a period where the hunting for the nails of Christ's cross, the spear that piercied his body, the cup from which Christ drank at the last supper, the bones of st. Paul, Peter and others saints was common. If the templars had purchsed the head of John the Baptist, this would be a sign of devotion to that saint. It is nothing different from the relics possed by other orders or institutions. (for example;The shroud of Turin) And on the ground of even remotely possessing it would not have made then heretics, but collectors of religious relics.
Spitting on the cross?
How about spitting on the cross was this not a sign of herecy? This reference is twisted out of context. A thing king filipe used to convict the templars of herecy.
The reality of the fact is totaly different. Templars used the spitting and desecration of the cross as a test on new members. To see if they would be able to stand up against torture and persecution, in case they would fall in the hands of pagan saracens, who would obviously try to convert them to their demonic religion. During such a test would come out, if the accolate had enough selfsacrifice and/or willpower to be a future templar or not. Any who would fail the test, and did spitt on the cross or deny his faith, would not be suited for a life of martyrdom within the order and thus be expelled.
(The Templars - History & Myth by Michael Haag, page 230 paragraph 3)
isis tells Christians to spitt on the cross [http://www.paulgolding.uk/spit-on-the-cross-or-die-isis-tells-christians/]