Speaking to The Telegraph after the motion was passed, Eddie Reeves, a Conservative councillor and leader of the opposition, warned the “vague” proposals could mean creating new facilities in anywhere between 200 and 600 buildings.
He said: “We all believe that being kind to people who are trans is right, but you can’t tell me I’m transphobic because I raised questions surrounding practicalities.
“It is a huge capital spend that is being advocated here at a time when the council already has too many buildings.
“It would probably cost hundreds of thousands – it will at least be a low six figure sum.
“I came up with a figure of around 170 – 270 buildings that the council has a direct interest in as a freeholder, counting all the ones we lease that is around 600.”
It is not clear at this stage whether the policy will also apply to schools.
Mr Reeves added that the plans would need to come back to cabinet once the costs had been finalised before they got the go ahead.
A spokesman for Oxfordshire County Council said: “As a result of this motion being approved, officers at the county council will now begin work on this detail and a resulting report will be presented to a future meeting of the council’s cabinet later in the year.”