Avila said regarding Freemasonry that "However, in the higher up levels, the theology starts getting really funky." Freemasonry comprises but three degrees or levels: Entered Apprentice (1st), Fellow Craft (2nd), and Master Mason (3rd). The "higher up levels" or "higher degrees" are those conferred by groups (such as Scottish Rite and York Rite) which are appendent bodies and not actual freemasonry.
The relationship of these appendent bodies to Freemasonry is like that of the Knights of Columbus to the Cathoic Church. You must be a member of the Church to become a Knight, but the Knights have no authority or power over the Catholic Church. Likewise, you must be a Master Mason to join a Masonic appendent body, but persons who have received the "higher degrees" via an appendant body have no authority, precedence or rank over any Master Mason. The degree work in those bodies expand on the lessons taught in the first three degrees. If one ends his membership in a Masonic Lodge, his membership in any appendant body also ends.
Freemasory is not a religion, but does have a religious basis. As for a "theology," there is none per se in any Masonic degree other than a firm belief in God. We have ritual, and we teach about our basic tenets--Brotherly Love, Relief, and Truth--and the cardinal virtues--Temperance, Prudence, Fortitude, and Justice. We do not teach a way of salvation, although one may infer from our ritual and writings that we espouse a way of living that may lead to salvation (the "good works plus faith" versus "saved by grace alone" argument). Freemasonry provides a means for a Christian--and any other religious person--to put their faith into action. As for whether such good works will lead to salvation is up to that person's religious beliefs.
Freemasonry has no religious requirements other than a candidate and member must believe in the existence of a superintending supreme being. An atheist cannot become a Mason. We instruct that a Mason should be regular in his house of worship, whatever and wherever it may be. For us, one's religious beliefs are a personal decision; no man, entity, or state has the right to tell a person what he or she must believe. In fact, discussing religion within a Lodge is expressly forbidden because of the discension it can cause.
In a Masonic Lodge, a volume of sacred law (VSL) must be opened on an altar in the center of the Lodge room when the meeting is started and closed when the meeting is closed. In predominantly Christion countries, the VSL is the Holy Bible. Masonic ritual is based on the Bible.
Some of the Christians who are against us say that we "deny" Jesus because we do not recognize him in Lodge ritual or prayer (i.e., we do not say "In Christ's name" or similar at the end of a prayer). We do not deny Jesus any more than we deny any other religion, prophet, or messenger of God. Freemasonry does not favor one religion over another. Thus the use of "Heavenly Father," "Supreme Architect of the Universe" (coined by Rev John Calvin) and so on in our prayers. This allows each member to pray to God as he knows him to be.
The York Rite of Freemasonry is based on Christian principles, with the top degree being that of Knight Templar, commerating the Knights Templar that fought for and protected the Holy Land during the Crusades.
The Rose Croix (Rose and Cross) degree in the Scottish Rite relates to Christ's crucifixion. There are services on Maundy Thursday, and on Good Friday the lights in a Scottish Rite Lodge are extinguished in commeration of Christ's passion and death. On Easter Sunday the lights are relight during a ritual to commerate Christ's arising.
I have been a Master Mason for over 19 years, am a 32nd Degree Scottish Rite Mason, and am Master of a Lodge. No where in any of the degree work or ritual have I seen or heard anything that contradicts Christ's teachings.