The few who did ended up regretting it.
The minute you are labeled and pigeon holed, someone will find the craziest, most whacked out person who they claim represents your religion and try to associate you with it, all based on the alleged fact that they are allegedly part of the same denomination.
And there is the identifying people issue. In some cities where there is only one or two churches of a particular denomination, something like Calvary Chapel, or Assemblies of God, if the person revealed their denominational affiliation, it would not take a lot of work to figure out who they were, and who needs anonymous internet stalkers making their lives hell?
Of course, even that is not a valid reason for some.