Meredith Lowell, who has a history of orchestrating similar attacks, is being held on a $1m (£775,000) bond after Wednesday’s incident in Cleveland Heights.
The victim had taken children she was babysitting to the church for choir practice – and Lowell allegedly stabbed her twice in the arm and once in the abdomen with a kitchen knife.
Lowell was wrestled to the ground by a member of the public and restrained until officers arrived, a police report said.
Police chief Anne Mecklenburg said the victim is still in hospital and her condition is unclear.
It has not been confirmed whether the coat that the victim was wearing actually contained fur.
Lowell, 35, was arrested last year on suspicion of attacking someone she believed was wearing fur at a Whole Foods store in University Heights.
A police report said she punched a woman who was wearing a jacket with fake fur on its hood – and then tried to cut the victim with the serrated blade of a Swiss Army knife.
Lowell pleaded not guilty by reason of insanity last month and the case is pending.
In March 2012, Lowell was indicted in federal court in Cleveland after authorities said she posted on Facebook that she wanted to hire a hitman to kill someone wearing fur and was willing to pay up to $850 (£658).
An undercover FBI agent contacted Lowell, who asked that a person be killed with a gun or a knife at a Cleveland Heights library and that she planned to be there when the murder was carried out.
Lowell told the agent she wanted to set up an animal rights militia and specified that a victim at the library should be at least 12 years old and at least 4ft tall.
Those charges were dropped in January 2013 when it was determined she could not be “rehabilitated to competency”.