In this document, EMFJ claims that Freemasonry in its third degree "baptizes" members to believe in, and imitate, the mythological character Hiram Abiff, and that Freemasonry regards this imitation as a way to achieve salvation. It further alleges that the 3rd degree of Masonry is a sort of pagan baptism into a non-Christian religion.
EMFJ defines baptism as:
"any experience that cleanses a person, or introduces him into a new kind of life."
Please note that with this definition, almost anything can be called a "baptism", e.g. school graduation ceremonies, weddings, reception in the boy scouts, or promotion to a new position at work. None of which mean that we enter into a new religion. Thus, the given definition is meaningless.
More compelling is the assertion that the 3rd degree involves "death, burial and resurrection" much in the same way as a Christian baptism. However, many things set the 3rd degree quite apart from baptism:
Anyone who has studied ethnology will know that "rites of passage" are a universal human phenomenon. Most of them mark and celebrate the natural stages in life, such as puberty, marriage, childbirth or death.
These basic rites are usually connected to the traditional religion of the participants. (Even Christian baptism was designed to replace the Jewish rite of circumcision.) Where religion has been outlawed by communists, non-religious rites of passage have been invented because there is still a need for them. Such rites have existed since the Stone Age.
With development of human culture, the idea that a rite is needed has spilled over into other aspects of life than the biological "passages", e.g. into dubbing of knights, school graduations, award presentations, presidential investitures etcetera. In medieval craft guilds, there were ceremonies to mark the passage from apprentice to journeyman, and then to master.
The 3rd degree in Freemasonry is a rite of passage within Freemasonry. It marks and celebrates that the Mason has passed through his apprenticeship and fulfilled his time as a fellow craftsman. The ceremonies are modelled on traditions that were used in medieval craft guilds, such as the Stonemason's guilds. To call this a "baptism" and portray it as a mockery of Christian baptism, as a sacrament of conversion into a new religion, is far-fetched and mistaken.
The anti-masons step even further out on thin ice when they assume that this "baptism" is undergone by people who have no idea of what they are doing. In fact, such things are described by St Paul in his letters, and his conclusion is clearly that if you participate in something pagan without being aware of it, it is null and void.
In Paul's case the question was whether a Christian could eat meat that had been sacrificed to the pagan gods. In the Roman empire, it was customary to make the slaughter of any animal into a sacrifice. Basically, any food served in the home of a Roman might be sacrirficial. Many Christians thought that it would be idolatry to eat such food. Paul answers this in 1 Korinthians 8. He says that if you eat sacrificial meat, the meat in itself does not harm you. It is only if the host, when serving the meat, proclaims that it is sacrificial, that Christians must abstain. Thus, only if you have been told that you are participating in a pagan ceremony, it is your duty to say no. If nothing pagan is said, then it is not a pagan ceremony.
The point is that even if the 3rd degree ritual was secretly a baptism into a pagan religion -- which it is not --- it would mean nothing to a Christian because it is not proclaimed as such by Freemasons, either externally or internally. It is only through a far-fetched interpretation of some words in the ritual that EMFJ reach their conclusion. Masons themselves do not interpret it that way.