Officially the Eastern Orthodox do not subscribe to the term “transubstantiation” either as a means to describe the Real Presence. Transubstantiation was an Aristotlean scholastic term. The Anglicans reject an official embrace of transubstantiation. The 39 Articles condemn it outright but keep in mind the 39 Articles are only normative in the Church of England and many provinces/dioceses/parishes do not accept the Articles as necessary or even true. Anglo-Catholics especially reject the Articles. Most Anglo-Catholics I know have absolutely no problem whatsoever accepting transubstantiation as a great term to define the R.P. The groups that don’t tend to be the evangelicals who lean toward a Genevan Calvinist model really.
Anglicans are not forbidden to take communion in Catholic parishes. It is the Catholic Church that forbids Anglicans to do so. And Anglicans, out of respect, comply and do not partake of your Sacrament. My rector and I were talking the other day about this. He told me he has visited Catholic parishes on many occasions and that he wishes greatly that he could go up and share communion with Catholics. His son is at West Point Military Academy and he visits a Catholic parish daily for Mass. He told the priest that he’d like to take communion, that he was an Anglican, that his father is an Anglican priest. The Catholic priest, rightly, told my rector’s son, “sorry, you may not.” Catholics have too many differences with Anglicans and historical divergence as well as an unwillingness to accept Anglican orders so they forbid Anglicans. Anglicans, however, would not forbid you from taking communion at their church. If you attended an Anglican church tomorrow, you’d be welcomed to the altar to experience the Sacrament.
Anglicans believe in the Real Presence but choose not to define the HOW of it, just that it is what Christ said it is: His Body and Blood. Queen Elizabeth I, who did a GREAT DEAL to define modern Anglicanism, believed in the Real Presence of the Eucharist but chose not to define “how” Jesus made Himself manifest in the Sacrament. She is famous for this saying about the Eucharist:
***Christ was the word that spake it.
He took the bread and break it;
And what his words did make it
That I believe and take it. ***