I am answering the question from a view of a Freemason with some rebuttal
Freemasonry is a fraternity that does not refuse people due to their specific religious preferences. But there are some exceptions. For an example, an atheist is strictly and universally (under the grand lodge of England) not permitted to join. Because we allow multiple faiths, some people take issue with the fraternity. Such as Christians are taught to not to yoke with unbelievers
This mortal hatred of the Church, of Christ, and of His Vicar on earth is not just an outburst of misguided individuals, but rather a systematic action that proceeds from the principle of Freemasonry: the destruction of all religion, but especially the Catholic religion. [Pisma Ojca Maksymiliana Marii Kolbego franciszkanina, Niepokalanow, maszynopsis, 1970; English tr. from The Immaculata Our Ideal, by Fr. Karl Stehlin (Warsaw, 2005), p.39]….
I have several friends who are Muslim, Jewish, Zoroastrian, etc. In the US, 90% (or more) of the people in the fraternity are Protestant Christian. I personally take great pride in the fact that I can talk to people of other religions, when appropriate, on level ground. It has helped me identify what I believe it is to be religious. Where on Earth can you get people of multiple faiths together, eat dinner, enjoy entertainment, and are friendly with each other? In my humble opinion, we need more of this today.
Tolerance to people of different faiths is not a Christian attribute. Christians hold the belief that the only way to heaven is through the salvation of Jesus the Christ. With this in mind, consider the words of the French Freemason Yves Marsaudon:
In our time our Br[other] Franklin Roosevelt demanded for all men the right to worship God in accordance with their own principles and according to their own convictions! That means tolerance and also ecumenism. We Freemasons of tradition will allow ourselves to clarify and revise these words of a famous statesman as follows: Catholic, Orthodox, Protestant, Israelite, Moslem, Hindu, free-thinker, free-believer–these words are for us only first names. Our family name is: Freemason.
My brother Marsaudon sounds very American and tolerant, however heretical to orthodox Christianity because it has a tone of Pantheonism. I have never met more pastors, rectors, fathers, clergy, etc than before joining Freemasonry. In my specific lodge, we have Episcopal rectors, a Presbyterian pastor, and a member of the Catholic clergy. It is important to note that Freemasonry does not attempt to be a religion nor a substitute for a religion. No matter how many books Dan Brown writ es.
At times Freemasonry is the scapegoat for anything that doesn't go the way of the church. Such as mentioned in the article Dechristianization
In the 19th century, the promotion of cremation in Western societies was favored by Freemasonry and materialism.
I can assure you that I've never heard of any Freemason promoting cremation except maybe one who has that process as their profession.
On a personal level there is a hysteria about Freemasons. Basically, we don't know why we don't like them but darn it, we hate them! As seen in @Bruce Alderman's link:
Now, let me make clear I am not “against Masonry.” I know too little about it to be against it. Rather, I’m perplexed. First, I was raised to believe that the church is one’s extended family, the family of God, and that one’s energy should be devoted to its ministry and mission first and foremost. Second, I was raised to believe that membership in secret societies is not compatible with biblical Christianity. It would be like an early Christian belonging also to a mystery religion; it wasn’t encouraged (to say the least). Third, I was raised to believe that Masonic Lodges were competitors with the churches even if many Masons also belonged to churches.
So any group that is not the church which you spend time is fair game to be anti-Christian per his logic. I hope your church has a lot of golf outings else you may as well sell your clubs. Forget joining that yacht club... etc.
What do people think? That Masonry is secretly adding members to "trick" them into worshiping their own god? That there's a time when you've received the 30th degree that someone says, "HA! Joke's on you! You were really worshiping Baal all along!" which at that point the mason just says, "oh, okay, cool!" Really guys?
**TL;DR**
Christians who do not believe you should be friends with non-Christians would have a problem with the fraternity. However you could apply that to your occupation or gym as well. If you don't want to work out with non-Christians, then maybe the public gym isn't one that you should join.
Freemason takes obligations or makes promises which some Christians dislike. So for example, I promise to not allow an atheist to join. Some Christians feel that you should not make promises like that to yourself or in front of God. However, the promise of marriage is a promise between you, your partner, and in front of God. The ceremony is not defined in the Bible; the promise to God is inserted by man. It is also a promise that's more frequently broken and forgiveness is then requested.
If you can be friends with Christians and non-Christians. If you have no problem promising to be faithful. Then you can be a good Freemason if you choose.