ANKENY, Iowa—Iowa is the spot where Donald Trump stands his best chance of turning a blue state red, but Hillary Clinton’s campaign team is aiming to quell that possibility by turning loyal Republicans into Democratic voters.

At households where voters have long participated in GOP primaries and caucuses, Clinton volunteers are knocking on doors asking for the women in the house. The Democratic nominee’s aides also are sending mail to Republican women and advertising to them online with reminders to vote.

Liz...