The Rundfunkrat appoints the Intendant who in turn has autonomy when it comes to programming.
I'm not saying that there's nothing to criticize about the structure but it was especially created in this way to provide checks and balances and not giving politicians direct control over the news. When some tried that in the past it made the news [2].
I think a right wing government would have an easier time defunding and replacing it with its own propaganda channels instead of using it for propaganda.
[1] https://de.wikipedia.org/wiki/Rundfunkrat [2] https://www.spiegel.de/politik/deutschland/zdf-anruf-wird-zu...
Links are in German.