So do electret mics have polarity? The following circuits seem to contradict each other...
Now the problem is one image shows polarity while the other one does not!! What's the holdup here?
Yes, they have polarity and it has to be right to work- the output needs to be biased positive with respect to the ground terminal.
The ground/GND terminal should be common with the case, so you can check polarity with a multimeter.
Here, from a Panasonic Datasheet, is a typical arrangement:
The two diagrams you show are equivalent, one is just drawn upside-down (potentially.. as it were.. confusing and not to be encouraged, but still valid).