The Chinese Communist Party has no branch in Taiwan, and has no intention to open one, since to do so would conflict with its policy of “one country. two systems”. Mr. Dai’s organisation is not affiliated to the CCP.
There is another communist party based in Tainan that was set up several years before Dai’s group. The way the then KMT government chose to deal with it was not to allow it to register as a legal political party, but not to disband it or punish its members, either. Since the party could not register, its chairman stood in elections as an indepedent.
I do think it ironic to see the DPP administration trying to enforce oppressive KMT laws from the martial law era ([url=Interfering in another country's internal affairs the first time[/url]).
Someone should tell Comrade Dai that sex discrimination in employment goes against the principles of communism.