I have seen a priest I respect well make exceptions for uncovered hair and imperfect dress (never anything totally scandalous, things that would be "dressed up" for NO).
He once mentioned in a sermon that someone's first time should be a welcoming experience, and we can sort out the details later. He also urged us to make sure that when we invited people they knew what to expect. The reasoning seemed to be that a lot of people flat out don't know, so we need to teach them, not reject them.
Every time I've seen a woman with uncovered hair receive, it was a first-timer who was back the next week with a veil. I think he probably spoke with them after Mass.