There's a bigger logical flaw: "belief that subjective opinions not based on evidence are acceptable" is an ambiguous English phrase. It can mean belief that:

1) if X is a subjective opinion, then X is acceptable.

2) there exists at least one X such that X is a subjective opinion and is acceptable

Needless to say, the argument depends on it being #1, while most people who would say such a thing would mean #2.

I believe that hairdryers are for sale at Wal-Mart. That doesn't mean that every hairdryer in existence is for sale at Wal-Mart.