In 2010, at a public event hosted by the Karunanidhi government, actor Ajith Kumar famously stated that actors shouldn't be forced to take a stand on sensitive issues. As he made the remarks, Rajinikanth non-verbally extended his support right in the presence of Karunanidhi. His colleagues, Vijay (now a political stalwart) and Suriya, among others, were present.
In Tamil Nadu, raising voice against Karunanidhi or Jayalalithaa even respectfully was considered a sin by their sycophants. Political functionaries were let loose to avenge such remarks/moves. While the BJP gets bad publicity for allegedly targeting Bollywood celebs who talk against it, the actual suppression Olympics takes place in TN.
Ajith, as per many, did face consequences for that speech. There wasn't an official ban on him, but the period between 2010 and 2011 (until the government changed) was definitely cold for him. He faced pressure from industry unions, and some of his projects faced logistical hurdles. That was a shadow ban. Or, at least, an attempt at a shadow ban. His "don't give a damn" attitude, specifically his decision to dismantle his own fan clubs in 2011 to prevent them from being used for political leverage, only solidified his image.
