Do your criteria count for women who advance in politics after a divorce? If so, the best match I can think of is Vigdís Finnbogadóttir, the former President of Iceland. According to this
biography, she was divorced before being elected president. She also has a daughter, but one through adoption, so again I'm not sure if that's how you mean "childless". As for religion, I don't know what Iceland was like in 1980, but agnosticism may be a safe bet.
Someone already mentioned Tarja Halonen of Finland. She left the Evangelical Lutheran Church of Finland in the 1960's, and decided not to rejoin them. She married only after having won elective office, and (from what I can tell) her kids don't seem to be from marriages.
And I'll mention
Jóhanna Sigurðardóttir. Both have had very un-traditional relationship histories. I can't figure out when Jóhanna was divorced, but she's been in the Althing so long, I expect that she won at least one election between her divorce from her husband and her later marriage to her wife. She does have two kids, though.