Well, Bajoran religious figures aren't required to be celibate or unmarried or even particularly restrained.
As religious as she is, she doesn't actively preach, she just believes. I can't really see her at the front of the shrine actually leading the service.
On second thoughts Kira becoming involved in one of Bajor's religious orders makes sense. But you are right about your last point. From her discussion with Kai Winn (where Winn admitted she had a vision from the Pah Wraiths) I thought Kira was deeply spiritual but reluctant to tell others how to believe in the Prophets. So Kira being a vedek? Being a vedek implies a position of power and I personally thought Kira was a rather humble person and quite selfless. Kira and politics do not mix!