I’ve been to the Y, and at the moment it doesn’t seem overtly christian. But, as long as that “C” is part of the name, and especially as long as “Christian” is part of the mission statement, it can potentially become a lot more unfriendly to non-Christians.

That document you linked to says that some YMCAs are overtly christian, and talk about the problems that causes:

Ys that have a strong Christian identity may find that non-Christians are uncomfortable with explicitly Christian language, imagery, and activities. Proselytism is an especially sensitive issue.

For example, several survey respondents express discomfort with colleagues offering Christian prayers or reading Bible verses during the “mission moments” that begin Y staff meetings