Well why shouldn't they, actually? According to your statements, I would think you would be glad we were opening our Mysteries up to more Christians.
Yes I would be happy if we offer Eucharist, as Christ did, to all, not as we pick and choose. What is deplorable is that we offer it to those who deny that Jesus is fully God and fully Man, MarMema, but we deny it to those who say "and from the Son" even though they share with us that Jesus Christ is Godman, with two distinct natures.