Dr Rachel McKinnon hit back after 1980 Olympic silver medallist Davies joined tennis icon Martina Navratilova in arguing transgender athletes have a "male sex advantage".
Twitter erupted after McKinnon said: "I guarantee that if we posted this photo and asked, Do you think it's fair for this transwomen to compete in women's sport? A LOT of people would be screaming NO and calling her a man.
"It's sad to say, and I don't condone it, but the people most happily supporting Sharron Davies's transphobia would be the first to call her a man if we showed them her photo and said she's trans. They would also use the 'eyeball test' against her."
One swim fan criticised "bully" McKinnon for "plain disrespect to an awesome woman".
Another tweet accused the bike ace of "ignoring the arguments and slinging meaningless insults instead".
And one claimed: "It is OK to disagree on this issue but this is a personal attack and not ok".
But supporters of transgender competitors insist most of the backlash against McKinnon's comment was "transphobic".
They claim arguments popularised by Davies and Navratilova are based on prejudice or unscientific assumptions, rather than any evidence.
And many felt McKinnon's tweet was just pointing out how some people make unfair "eyeball" judgements on certain athletes.
One reply to McKinnon read: "I get the point you're making and I think it was neatly done.!"
A Davies' supporter responded by tweeting a photo of the TV star in a swimsuit at the peak of her career, saying: "This is the trained body of a female Olympic swimmer.. whose athletic credentials are beyond reproach.
"You undermine any respect by this childish vitriol against her."
But that message prompted the reply: "You could mistake this woman for being trans even in this photo. There's nothing wrong with that."
And McKinnon herself added: "Yup. that's my point. The very idea of the 'eyeball test' is misogynistic and gets used against cis women, too."
Today's Twitter row is the human side of a debate that has split sport.
Davies had originally fuelled McKinnon's ire by saying: "Have nothing against anyone who wishes 2be transgender.
"However I believe there is a fundamental difference between the binary sex u r born with & the gender u may identify as.
"To protect women's sport those with a male sex advantage should not be able 2compete in women's sport."
Scientists are trying to establish if transgender women still have a physical "advantage" after taking medication to reduce male levels of testosterone.
The International Olympic Committee says these athletes can compete if they have been lowering the amount of testosterone in their body for one year.
But Fair Play for Women argue the IOC is overlooking evidence that transgender athletes retain an improved performance – due to a “legacy effect of testosterone”.
In turn, transgender competitors counter this by arguing there is no scientific evidence supporting this theory – and that in fact there is no advantage at all.
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