The 50-year-old dancer and choreographer told The Mirror that he'd been stunned to receive nasty messages after declaring in an interview that he and partner Damon Scott were considering adopting in the future.
"Some people have been really horrid and abusive and disgusting. There are kids out there who need education and they need foster homes to go to and they need people who are prepared to love them," he said.
"A gay couple can offer that as much as a straight couple as they can't have children naturally. I don't know what the big fuss is about."
Craig and Damon have been together since 2013 and currently live in Hampshire.
Last year, Craig said that meeting Damon – a former Britain's Got Talent star – had been the best day of his life.
"When I met Damon for the first time, at a karaoke bar in Southampton, I'd been having a very stressful time doing Fiddler on the Roof," he told the Express, "so a few of the boys and I went out on the Sunday night and I bumped into Damon.
"That's when my life changed for ever."
Craig is currently preparing for the launch of the Strictly Come Dancing 2015 Live Tour, which begins this month in Birmingham.
Contestants performing this year are the show's winner Caroline Flack, Frankie Bridge, Thom Evans, Mark Wright, Alison Hammond, Simon Webbe and Scott Mills.
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