Dr Rizwan Mustafa shared content promoting the destruction of Israel and described Jews as “filth”, according to an official report on the Government's anti-terrorism strategy Prevent.
The matter was put forward for investigation by West Midlands Police and Crime Commissioner Simon Foster. He said that after a "thorough" probe that had treated the matter with the "seriousness that it required", the force had concluded that no further action would be taken.
West Bromwich East MP Nicola Richards has written to the Security Minister criticising the decision, saying the position adopted by the police was "unacceptable" and would damage relations with the Jewish community.
In a letter to , Mr Foster said: "West Midlands Police have concluded that, in their view, neither the material referenced in the independent review of Prevent, nor the manner in which it was shared, contravenes Section 58 of the Terrorism Act 2000 or the Public Order Act 1986.
"As a consequence, West Midlands Police have determined that they will not be taking further action in connection with this matter."
Dr Mustafa currently holds a senior position at Staffordshire University as the police training lead. He was a police officer for 10 years and was founding chair of the West Midlands branch of the National Association of Muslim Police.
The Shawcross review into Prevent, which was published by the Home Office in February, said Dr Mustafa had "shared conspiracy theories" about the origins of al-Qaeda and Islamic State.
It included a video that contained a "call" asking: "Where is the Caliph of the Muslims? Don’t you care that the Jews are defiling the place of the prophet’s nocturnal journey with their filth? The Jews are the most hostile people towards the believers."
Conservative MP Ms Richards, who is chair of the APPG on anti-Semitism, has written to Security Minister Tom Tugendhat regarding the decision.
She said she was "shocked" that West Midlands Police had "not even attempted to condemn the views" expressed in the posts.
She wrote: "The position adopted by the police is unacceptable and must be challenged, not only because of the damage this decision will cause to the Jewish community's faith that they would be treated fairly by the police, but also because Dr Mustafa held security clearance and a role within West Midlands Police where he advised officers on counter terrorism strategy."
Ms Richards added: "I will not accept that West Midlands Police would condone such views, or that no further investigation is required into his actions within the police whilst he had security clearance."
West Midlands Police has been contacted for a comment.