1. When one's acts or speech are supportive of a position, group, or event; especially when such support is (or appears to be) atypical.
2. Dressing up for a formal event.
Although Parker is generally critical of religion, he puts-his-tie-on for Mormons, for whom he has profound respect.
I generally like dressing like a slob, but I put-my-tie-on for Grandma's funeral, to show my respect.