Many traditional bigotries have centered around obvious physical characteristics: race, ethnicity, gender, etc. Because of this, some claim that there can't be any serious bigotry against atheists because an atheist isn't defined by any obvious physical characteristics. You can't pick an atheist out of a crowd and you don't even know someone is an atheist unless they say so. That, however, is part of the problem for atheists: their invisibility helps perpetuate myths and suspicion about them.
The first obvious problem with this attempt to dismiss the existence of anti-atheist bigotry is the simple fact that here has been plenty of bigotry, prejudice, and discrimination against people on the basis of characteristics that don't allow for them to be readily singled out in a crowd. It's rare that you can look around and single out people by their religion, sexual orientation, political beliefs, etc., but past bigotry and discrimination against them is undeniable.
The truth is, you don't need to be singled out in a crowd for bigots to hate you and it's unreasonable to set this up as a standard for who is and is not subjected to bigotry, prejudice, or discrimination in society. If anything, the invisibility of a group can contribute to their continued oppression on a number of levels. When people don't see members of this minority around them doing all of the same things as others, it's difficult to remember that they really do live much like everyone else. When members of this minority are invisible, their interests, needs, and problems can be ignored as well.
Viewed from the other side, the general invisibility of atheists makes it that much easier to remain invisible — to stay in the closet and thereby avoid even worse experiences at the hands of their loving, religious neighbors. Ethnic and racial minorities rarely have any choice about appearing in public as who they really are, but others do — Jews, gays, and atheists are all groups in which many members have chosen to "pass" as members of the majority because it can make life easier. In some cases, light-skinned blacks learned to "pass" as whites in order to be treated with the basic dignities and decencies not normally accorded to other members of their race.
Unfortunately, "passing" like that ultimately serves to make things worse in the long run. Atheists would be invisible enough without them actively hiding it, but hiding compounds the aforementioned problem of no one seeing atheists for who they really are: normal people who live normal and moral lives. Gay rights activists recognized this problem and it was a major impetus behind encouraging as many gay people as possible to come out of their closet and be open about their true sexual orientation.
Being quiet and inoffensive never provided any benefits to the gay community, never deceased hatred of gays, never educated people about gays, and never advanced the cause of equality a single iota. The same is true for atheists, though they are only now slowly coming to this realization. As with gays, atheists are being informed by helpful religious theists that if they just kept quiet and weren't so uncivil in their criticisms of religion or theism, then people wouldn't despise atheists so much — as if atheists were loved when they hid.
What religious theists fail to realize — probably because as part of the majority they have never had this experience — is that being told to be quiet is itself part of the system of anti-atheist bigotry which we have to deal with. Thus their "advice" isn't so much a means for helping us as it is for keeping us locked into the very system of unjust privilege which they so amply benefit from. How can atheists be subjected to bigotry if they can't be identified? The answer is simple: by ensuring that they don't want to be identified out of fear of the repercussions, and by advising them to keep quiet about who they are in the hopes that silence will buy a little security.
