Before mass began today, I was told that one of our songs for the mass, "All Are Welcome," was banned by a bishop in Wisconsin because he believes it gives the wrong message. He says that not everyone is welcome to receive the Eucharist. Those who have committed a mortal sin, or who have not been brought into the Catholic Church through the Sacraments are not to partake of the Eucharist. While it is true that people aren't supposed to take the Eucharist if they don't fully understand its implications (through the Sacraments) or while they are still in a state of sin, this does not mean that they are not still invited.
I think of it like a transplant recipient. When on the list to receive donor organs, recipients have to realize that receiving the organ requires that they change their lifestyle (at the very least, they will need to take anti-rejection medication for the rest of their lives). More so, possible recipients who demonstrate that they aren't going to stop the unhealthy behaviors that led them to their current condition, such as non-rehabilitated alcoholics looking to get a new liver, are also denied access to these limited, precious organs.
The same is true for the Church. All are invited to eternal life, but it means that we need to be willing to change our unhealthy habits and do what Christ asks of us. Pope Francis was cheered when he said that homosexuals and atheists were still invited to heaven, but then jeered when the Vatican noted that there are conditions to this invitation. God loves all of us and wants all of us to be with Him for eternity. Yet we have to do our part as well. We don't need to be perfect, only Jesus is that; we do, however, need to reciprocate His love.