Stephen Meeneghan, a naturopathic doctor, was hesitant when he received a message on a dating app from Ryan Cassata, a transgender advocate and musician. Yet they clicked right away.

Jason Mercado and Kristen Bateman, who met 10 years ago, didn’t begin dating until after three months of emailing. “I wanted to become friends first,” Ms. Bateman, a self-described introvert, said.