Hussar
Legend
Nothing prevents a bard from using a holy symbol or having faith either...
So, sure, a bard could look like a cleric, sans the heavy armor of course, and different weapons, and the singing bits, and the fact that while he has a holy symbol, he never actually uses it, but, sure, a bard could look like a cleric. Doesn't have to though. Nothing in the bard description ties a bard to any faith at all.
Put it another way, a cleric without any holy symbols, and never once references his or her faith would be something of an outlier. Most clerics are going to be pretty recognizable. That there might be a chance that some other class, for whatever reason, wants to look like a cleric doesn't really change that.