Jehovah's Witnesses cannot join the YMCA.
The Sept 1885 Watchtower took the position that joining the YMCA is wrong. They said, '“Alas for the Bible-rearing practiced in the Y. M. C. Associations! They are completely under the control of the sectarians, by whom they are supported. Though professedly non-sectarian, professedly controlled by no creed but the Bible, they are more creed-bound than others, since they are bound by all the popular creeds.”'—P. 6.
Later the underlying religious purpose and interfaith efforts of the YMCA was mentioned in the September 1964 issue of Kingdom Ministry, - a publication used by Jehovah’s Witnesses at their meetings.
JW's believe all churches and governments are part of Satan's organization. Therefore involvement with any Christian organization such as the YMCA would be 'apostasy'. Since 1925 WBTS has been giving JW's only two choices, - the Watchtower organization or Satan's organization.
WT Quotes About The YMCA. Jan 1, 1979 Watchtower Magazine.
Question From Readers: 'Is it true that for religious reasons Jehovah’s Witnesses may not become members of the YMCA (Young Men’s Christian Association)?' 
Answer: 'Yes, that is so. We have long recognized that the YMCA, though not being a church as such, is definitely aligned with the religious organizations of Christendom in efforts to promote interfaith.' ... 
'Many persons think of the “Y” simply as a social organization that offers various services, such as a swimming pool, facilities for athletic training and a place for clubs to meet. Commendable as some of these provisions may be, it is important to bear in mind that the YMCA was founded with a distinctly religious basis. This was set out at a World Alliance in Paris in 1855. The main part of that official statement (called the Paris Basis) reads: 
“The Young Men’s Christian Associations seek to unite those young men, who, regarding Jesus Christ as their God and Saviour, according to the Holy Scriptures, desire to be His disciples in their faith and in their life, and to associate their efforts for the extension of His Kingdom amongst young men.” (Italics added)  
'While in some countries churches may not be the YMCA’s main source of revenue and while membership is open to persons of all races, nationalities and religions, the fundamental religious objectives of the “Y” cannot be ignored.' 
'‘But,’ some may sincerely wonder, ‘is religion or interfaith really an aspect of the YMCA?’ The answer must be “Yes.” Though religious features may be de-emphasized in some branches of the YMCA, all local “Ys” are still expected to comply with the Paris Basis.' ... 
'Consequently, there is ample evidence that the YMCA originated with religious objectives and continues to have such to this day.' 
'In joining the YMCA as a member a person accepts or endorses the general objectives and principles of the organization. He is not simply paying for something he receives, such as when buying things being sold to the public at a store. (Compare 1 Corinthians 8:10; 10:25.) Nor is his membership merely an entry pass, as when a person buys a theater ticket. Membership means that one has become an integral part of this organization founded with definite religious objectives, including the promotion of interfaith. Hence, for one of Jehovah’s Witnesses to become a member of such a so-called “Christian” association would amount to apostasy.' 
'Some individuals have on occasion not become members but have paid a onetime admission fee, viewing this as simply paying for a commercial service available. Even in this regard it is wise to consider whether this course will adversely affect the consciences of others.—1 Cor. 8:11-13.' 
How does the Watchtower convince JW's that associating with other Christians and attending other churches is wrong? They use the Bible.
The Bible says, 'Do not be yoked together with unbelievers. For what do righteousness and wickedness have in common? Or what fellowship can light have with darkness? What harmony is there between Christ and Belialb? What does a believer have in common with an unbeliever? What agreement is there between the temple of God and idols? For we are the temple of the living God. As God has said: “I will live with them and walk among them, and I will be their God, and they will be my people. Therefore come out from them and be separate, says the Lord. Touch no unclean thing, and I will receive you.' 2 Cor 6: 14-17
The YMCA and Political Neutrality.
JW's believe that because the YMCA has allocated resources for the spiritual needs of US soldiers since the Civil War, joining such an organization would violate the WT's position on political neutrality.   
JW's are politically neutral. They do not go to war. They will not defend their country. They don't vote. They cannot sing the national anthem or salute the flag.
1. 'Is it true that for religious reasons Jehovah’s Witnesses may not become members of the YMCA (Young Men’s Christian Association)? Yes, that is so. ...' Watchtower Jan 1, 1979, 'Questions From Readers'
2. 'YMCA services to the armed forces began, in the United States, with the Civil War, and it continued giving service through all wars thereafter.' —Encyclopædia Britannica, Micropædia, Vol. X, p. 835, 1976 ed.
3. “In the Civil War, only ten years after its beginning in Boston, and before there were buildings or secretaries or financial resources, a total of 4,859 ‘delegates’ were recruited and deployed and over six millions of donated funds used for the temporal and spiritual needs of soldiers. . . . In World War I, the American Y.M.C.A. assumed an enormous responsibility for service at home and abroad for which a staff of 25,926 was required with expenditures of more than 167 million dollars. In World War II, the Y.M.C.A. became one of the organizations that founded the United Service Organizations [USO], joining as a group of private religious organizations from Protestant, Catholic, and Jewish faiths in an agreement with the Federal government to provide civilian recreational, welfare, and religious services to men in uniform and to war-production workers in communities adjacent to military establishments.”—The New Funk & Wagnalls Encyclopedia, Vol. 36, pp. 13,467, 13,468, 1952 ed.
4. “YMCA activities for members of the armed forces began during the Civil War (1861-1865). These services increased with each later war and reached their fullest development during World War II (1939-1945). The YMCA maintained more than 450 clubs for the Allied armed forces.”—The World Book Encyclopedia, Vol. 21, p. 477, 1978 ed.
5. According to the 1855 document, World Alliance in Paris, the YMCA seeks to unite young men who believe Jesus is their God and Saviour. JW's don't believe Jesus is God. They believe that Jesus is God's son and Jehovah is God. They also don't believe in a Trinity.