… and with good reason are accepted as brothers in the Lord by the children of the Catholic Church" does not exempt them from any of the rules of the Church. … I see no exemption from the responsibility living their life and concluding it in the of grace. Do you?
Yes, they are exempt from some of the rules of the Catholic Church. For example, non-Catholics do not follow the Catholic form of marriage. They do not have to (and are forbidden) to receive the Eucharist once a year. Many of the laws of the Church do not extend past the visible membership
On a different level, there is no moral examption. In this you are correct that just to claim one is once saved always saved does not make it so. However mortal sin requires full knowledge of the nature of the sin. Sins like murder and adultery are obvious. Less obvious mortal sins (like contraception) may not be taught to these Christian brothers by their pastors.
In the end, our non-Catholic brothers will enter heaven for the same reason Catholics will, because they are in a state of grace.