We really need an Anti-Frankfort School, something which will actively seek out the Left and work to purge Leftist ideas from society.
To succeed with your idea would require identifying the most basic ideological foundation of the Frankfort School.
In my opinion, the ideas of the Frankfort School from which all others arose are not economic or even philosophical. They are spiritual.
The Frankfort School starts with hatred of God. So, love of God and trust in God is the only way to oppose them.