Wealthy environmentalist and political donor Tom Steyer is causing anxiety for Democrats by campaigning to kill the Keystone XL pipeline and criticizing Democrats who support it, according to Democratic lawmakers and campaign consultants.

But party leaders aren't giving Mr. Steyer the cold shoulder. Next week he will host a Democratic Senatorial Campaign Committee fundraiser for environmental alliance candidates at his home in San Francisco. Then he will fly to Washington, D.C., to moderate a panel at the Democratic Governors...