The answer is not as simple as ‘yes’ or ‘no’ when it comes to the question of whether Protestants are permitted to share in the Eucharist. Anglicans and Lutherans both believe in the ‘Real Presence’ of Christ in the Eucharist. Some Anglicans go so far as to believe in Transubstantiation. Clearly, it is not ‘just a piece of bread’ or a ‘memorial’ in either case. Furthermore, the Anglican and Catholic International Dialogue Commission, in a 1981 document entitled ‘The Final Report’, claimed in the sections relating to the Eucharist “to have attained a substantial agreement on eucharistic faith.”
Although members of neither denomination can regularly receive Communion in Catholic Churches, there are circumstances where they are permitted to do so, if they are otherwise properly disposed. In some circumstances, they may also receive in other pastoral situations, such as hospital visitations.
While I was still an Episcopalian, I did once mistakenly receive in a Catholic Church. A friend of mine, who is a Catholic, asked the celebrant about the situation, and was told that I should continue to follow my conscience on the subject, and that my receiving did not constitute a ‘great evil’ in the eyes of the Church.
On the other hand, the Church considers Anglican Holy Orders invalid, thus Catholics may not receive in Anglican churches.