So when Cate Blanchett rolled into town for a new adaptation of Anton Chekhov’s “The Seagull,” at the Barbican Theater, a little trepidation could be forgiven. But Blanchett is different.

Cate Blanchett can — and does, in Thomas Ostermeier’s terrific new staging of The Seagull. She also tap dances. It’s a dazzling performance at the heart of a superbly acted production ...