Back to the question of the headline: why can't a Protestant (or anyone else who isn't Catholic or Orthodox) come to Holy Communion? Why are Catholics so mean and elitist?
I will answer this way. Suppose you brought me a gift: a big, beautiful box. After I ooh and ahh, I open it up, and my eyes widen to see five or six objects in the box. I start pulling them out one at a time.
The first item I hand back to you. "No, I don't think so."
"I don't like that. I don't want that."
I pull out another item, and scrutinize it. "Hmm. Maybe, we'll see." I pull out another item. "No, not that either," as I hand that back also.
In the end, I keep one or two items and give the rest back to you; your smiles have turned to shock and you struggle for words as I say, "Oh, and I don't really want you, either. But these are nice!"
Now, tell me: in what world would my actions not be the height of rudeness? No one could consider this acceptable.
But understand, dear, dear Protestants: when you come to the Catholic Church, and complain that you don't get to take Holy Communion on your own terms, this is what you are doing.
The Holy Eucharist isn't a thing but a Person, a Divine Person; and we don't merely receive the Eucharistic Lord, we enter into communion with Him. And when you seek to be in communion with Jesus, He is, pardon the expression, a "package deal." Along with the gift of the Eucharist comes all the sacraments; and the Sacrifice of the Mass; and the priesthood; and the Magisterium (teaching office) of the Church, and, well, the whole Catholic Church as well. And the moral teaching of the Church, which isn't easy for most of us (any of us) and we all strive to live up to it, and we go to confession as we need to.
So, you want to receive the Eucharist? WONDERFUL! Here's the whole package; no, I'm sorry, it's really rude to say you reject the rest of the package and just want the Eucharist.