Protestants are “separated brethren”, not simply “brethren” because the churches are divided over various issues, including the Eucharist. Therefore, non-Catholics are not supposed to receive communion in Catholic churches (with a few, rare exceptions for Orthodox Christians, who wouldn’t receive anyway on account of their own rules).
Just so. Protestants and Catholics agree on many things—as do the numerous kinds of Protestants. But with the possible exception of High Anglicans, they disagree on the nature of the Eucharist. Catholics believe that it is, in substance, the real Body and Blood of Christ, and only in outward appearance bread and wine.
Since Orthodox Christians also believe in the real nature of the Sacrament, they may be allowed to receive it—but are forbidden to by the authorities of most Orthodox churches.
It would be wrong for a Lutheran to receive Communion, because Martin Luther denied the reality of the Sacrament. It is NOT the real Body and Blood of Christ. Most Protestants continue to take that position. How can they properly and respectfully receive the Sacrament when they don’t believe in it?
I once headed a scholarly conference on Christianity and literature that included both Catholic and Protestant (mostly Evangelical) members. We could work on many things in common, while agreeing to disagree on some theological points. The nature of the Sacraments was certainly one such point. But we could agree that marriage was between a man and a woman and that adultery was wrong, to take one area where we differed from many or most secularists.