So, the outwardly was important -- uniformity of liturgy, damn the doctrine! As long as everything looks good on the outside. But, alas, churches that don't teach the same doctrine are not the same churches. But who cares! As long as they all got together and worshiped the same queen!
Yup, that was the idea. But perhaps we should be a little more forgiving of Elizabeth: She was in Western Europe, where as St. Justin Popovic points out, the papacy had already replaced the God-Man, Christ, with a mere man, the Pope, as head of the church, and hers was the era that saw Western Europe racked by wars of religion. She ascended the throne after period of persecutions with non-papal and papal Christians in England taking turns as persecutors, and had memories of her father's horror at the prospect of dynastic wars. State compulsion in matters of religion was coming to be seen as a bad thing in north-western Europe. It was about the same time that the Netherlands became the only place besides the Serene Republic of Venice (which allowed both Latin and Orthodox churches to function freely on its territory) to not have a state-enforced version of Christianity. Elizabeth was concerned with the peace of her realm more than with deciding anything about religion. And, well, that was her job.
The real tragedy in the whole thing is that Henry didn't have any ties in the East. Had he aligned England with Russia (or more improbably Constaninople where the Turkocratia had already begun) his argument that a marriage to his brother's widow was illegitimate would have been held valid by the Orthodox since it violated Byzantine sensibilities about cosanguinous marriages, and he'd have had his annulment. Maybe if he'd done it right, leading England back the the Church instead of setting up on his own, God would have blessed him with a male heir, or a good court advisor, who could cite the precedents of the Empresses Irene and Theodosia to convince him that a queen could be a strong enough ruler to prevent the horror of dynastic war.
The only quibble I will make comes from limited personal observation:
Any or all of the persuasions may be very fond of the 1928 BCP.
In my experience, low church tends to prefer the 1979 BCP for its modern language (and given a choice of rites, the modernized Rite II therein). High church tends to prefer the 1928 BCP, or if stuck with the 1979 for whatever reason, Rite I (which is closer to the 1928) therein.
The Continuing churches, though, have a very strong preference for the 1928. (I'm not aware of any that use the '79.)