Someone once pointed out that there are lots of movies about conservatives seeing the light and becoming better human beings as liberals, but none of the reverse.

What counts? Is becoming more religious being conservative? Is becoming a member of a more traditional rural community becoming more conservative? I feel like people are going to stack the deck based on their own views when they answer a question like this.

The villain politicians in Mr. Smith Goes to Washington seem like they’re supposed to be New Dealers, trying to crush the little guy in a big government vs. small government showdown. They’re involved in a corrupt land development deal, which is something liberals believe only conservatives so, and liberals are more likely to want to blow the whistle on.
Screenwriter Sidney Buchman was blacklisted by HUAAC. Capra was a Republican. The movie doesn’t really fit your question regardless, because Jimmy Stewart’s character doesn’t change his political believes, he just uncovers the corruption of people he’d previously trusted.

If you want something that fits exactly what you have in mind, I think the liberal reporter in The Green Berets works, but I barely remember that movie.