Cold War era anti-communism did not draw distinctions between Soviet "socialism" and democratic socialism although the Soviets explicitly purged democratic socialist movements and organizations and preferred leaving Spain to the fascists rather than allowing them to come out on top.
Soviet "socialism" also isn't communism -- heck, the term "actually existing socialism" was coined to ridicule "utopian" leftists who wanted to achieve communism in Soviet-affiliated countries. Communism, a stateless society without private ownership, was always only considered the stated end goal of these countries, even when they actively took steps to prevent any progression towards that goal.
If Orwell's detractors have been right on one thing about Animal Farm it's that people on the right are too ignorant to treat it as anything other than a condemnation of all forms of socialism although he specifically wrote it to condemn the Soviet Union's corrupt bureaucracy and the exploitation perpetuated by all forms of statism, whether under the guise of fascism, Soviet "socialism" or capitalism. The actual morale is fairly straightforward: the pigs get corrupted because they try to replace the humans but the oppression stems from the system affording the humans (and pigs) their position, not their species. You can't replace one state power with another and hope this will result in the abolition of the state because the state exists to perpetuate itself.