We cannot give the Holy Eucharist to non-Catholics, because this is a contradiction in itself and undermines the true meaning of the Eucharist. It is a trivialization of the Eucharist and undermines the doctrine and the truth. The Holy Communion is the highest and fullest expression of the unity of all members of the Church. It is the highest expression of unity with the Church itself.
When someone does not accept all the truth of the Church and all its dogmas, not only the dogma on the Holy Eucharist and Transubstantiation, it is not sufficient. This includes all the dogmas about Our Lady, the Immaculate Conception, the papacy, the dogma of the primacy, and the infallibility of the magisterium of the Church and the Pope. When someone does not accept all of these, he is not in full union with the Church. There is a lack.
When he goes to receive Holy Communion at the same time, he is lying because he is still rejecting or not accepting the fullness of the Church. He is not united with all the truth of the Church, yet by receiving Holy Communion, he is showing that he is in full and complete union with the Church. This is a contradiction and a lie.