the logic is: "everything I don't like (gay people etc) is communism"
That's very uncharitable. The Epoch Times is explicitly anti-CCP; anti Chinese communist party.
It's also run by a cult.
Yes, but it's the "John Birch Society" form of anti-communist, not the "Solidarity" kind.
The CCP hardly qualifies as communist,
Their logic is that the US government behaves like a communist regime, doing whatever it can to punish and silence real dissent (like Edward Snowden and Julian Assange), so they assumed it might just be using this as an excuse to punish a newspaper that often hosts anti-US-government content.
I'd grant you that the US government acts like an authoritarian regime, but communist is a laughable accusation.