There are many ways to approach this one. For sake of brevity:
1) The Biblical idea of a society is the People of God (in the OT the Israelites; in the NT the Church). It seems, from this point of view, to be superfluous and "off-topic" to join another society when you are indeed a member of the Church. Such societies often bind believers with non-believers.
2) There are also many other reasons to beware such groups. Consider all the "appearances of evil" that are a part of Masonic history. If we are to be transparent, to be right before God, we must also avoid such appearances, even if they are not evil or actually sinful.
3) Personally, as a Catholic, we are forbidden to join or associate with Masonry due to its being a secret society that is not in communion with the Church. From that very fact one can deduce that whatever is secret needs be kept from Christian minds.