CathInfo.com

Not Paranoia, it's prudence. Before the Council, non-catholics knew they could not approach the communion rail, and you didn't have wanderers from the conciliar church walking into your traditional chapel thinking they can just go up.

The Blessed Sacrament has to be protected, so yes, there should be precautions keeping people from coming up and committing a sacrilege.

How would chapels enforce this? Announce at each Mass that anyone who is not officially registered in this chapel is not to receive Holy Communion?  It’s for members only?  What about receiving absolution? Forbid non-members from going to Confession? How would that be enforced? There could be signs all over posting the rules and they could be announced from the pulpit. Yes, but don’t be surprised if that chapel does not grow! It’s extremely off-putting. It’s not like the priest sees them and personally knows every one of them. Perhaps in a very small chapel he does. But what about mission chapels? Is a priest supposed to know by sight each and every “member” of the chapels he serves? 
What about truly traditional visitors? Is it right to deny the Sacraments to strangers just because they are strangers? What if a visitor is in mortal sin and NEEDS to go to Confession? Suppose he is prevented from that and on the way home, he is killed in an auto accident? He goes to Hell and it’ll be on the priest’s conscience. 
Perhaps the ushers could stand at the door and give color-coded tickets or tokens to members only. Red for Communion, Purple for Confession. When arriving for each, the ushers hold baskets into which each person drops his or her token?  
What would CI members do if you were traveling, wanted to hear Mass, and discovered this “system”? 
Personally, I’d assume I was not wanted and would sanctify the Sunday or Holy Day by myself. 

Fr. Ward, SSPX, when he was in Arcadia, CA would make an announcement at each Mass welcoming any newcomers informing them that only Catholics in the state of grace should receive Communion, and to receive kneeling and on the tongue. I always thought that was a good practice, especially considering the location of the Church in such as busy part of city. So other priests can do something similar, especially when they notice someone new.

That is perfectly reasonable. I was being facetious in my post about giving color coded tokens.  
If, after a simple announcement, a person not disposed to receive Communion goes anyway, it’s on his conscience, not the priest. The only time I can a priest skipping over them is if someone is very immodest or is obviously a public sinner, (wearing clothing, jewelry, and hair that marks them as LGBTQ or is otherwise inappropriate, looks outwardly bizarre as to draw attention to themselves, wearing a lobster costume, etc.) As for Confession, that needs to remain anonymous. 🦞