I do believe it is important, as you do, that a non-Catholic at Mass needs to understand that they are not to get up and receive the Eucharist. And it isn’t because we think we are better than them.
When one receives the Eucharist it is because they believe in everything the Catholic Church teaches with regards to the faith. One has to learn about the Catholic faith to understand what it teaches, and if they believe in it then become a member. Usually this is done via RCIA.
I have done readings at numerous funerals at my parish, and prior to receiving the Eucharist the priest would explain tactfully (I don’t remember how he said it), to those who were non-Catholics attending about remaining in their seats, or coming up for a blessing by crossing their arms over their chest. There always were many non-Catholics attending a funeral Mass for their Catholic friend.
One time a new priest forgot to explain about that to those attending the Mass and several non-Catholics came up to receive and it was very awkward at one point when someone took the host with both hands from the priest and hesitated and seemed confused and then put the consecrated host in their mouth.