B737 Captain reported refusing an aircraft due to a door girt bar not working properly.

Narrative

Inbound crew Aircraft X ZZZ wrote up forward service door girt bar being difficult to engage and disengage. Contract Maintenance was already working on it when we arrived at the aircraft. He adjusted it and had the FA (Flight Attendant) try it. She said it was still not functioning properly. He tried a few more times to adjust the bar; but each time the FA's said it was not working properly. The mechanic said that was all he could do with it and in conjunction with Maintenance Control signed it off in the logbook. All 4 FA's insisted that it was still not working correctly; so as it is an emergency safety item; I refused the aircraft. I was then contacted by the Dispatch to get the facts of the situation. After that I was contacted by the ZZZ1 Chief Pilot's office for more details about the situation. I then wrote an info item in the logbook to document the refusal. Cause: As a Captain I feel it is important for me to back up my crew; especially when it comes to safety equipment that they operate on a daily basis.