And we already know that the body of Christ where man should enter is His Church.

18 And He is the head of the body, the church, who is the beginning, the firstborn from the dead, that in all things He may have the preeminence. (Colossians 1:18, ibid)

But why is it that we should first become members of the Church of Christ for us to receive salvation through Christ? It is because Christ is the savior of His own body or Church:

23 For the husband is head of the wife, as also Christ is head of the church; and He is the Savior of the body. (Ephesians 5:23, ibid)

Therefore, those who said that Church affiliation has nothing to do with Salvation do not understand how Christ save man. It might be true that a man couldn't attain salvation if he is affiliated to the false church or those churches who are not of Christ. But those who are members of the true Church of Christ will surely attain salvation because Christ saves them and will save them on the day of judgment.