ALPHARETTA, Ga.—For years, Rachel Paule didn’t have much to do with politics. That changed abruptly after Election Day.

The 23-year-old Georgian attended the women’s march in Washington after President Donald Trump’s inauguration. She became a local captain for Sister District, a new online group that directs donors to legislative races around the country. She contributed $15 to a Delaware state senate candidate running in a special election more than 700 miles away.

...