A petition is up to persuade Pope Francis to hold the line on, among other things, the excommunication of Catholics who have remarried after a divorce. In part, it reads:
Your Holiness, in light of the information published on the last Synod, we note with anguish that, for millions of faithful Catholics, the beacon seems to have dimmed in face of the onslaught of lifestyles spread by anti-Christian lobbies. In fact, we see widespread confusion arising from the possibility that a breach has opened within the Church that would accept adultery — by permitting divorced and then civilly remarried Catholics to receive Holy Communion.
The thing about a mortal sin like adultery: there has to be a marriage in place, and among the parties involved, there has to be a willful conscious act to separate oneself from God. That divorce is widespread and routine for many people is truly lamentable. It’s bad on a number of levels: that people are ill-prepared to marry, they lack positive role models in the social contexts into which they are drawn (the mainstream video media including, yes, the Fox network), they abuse substances, they have been drawn into pornography and other behavioral addictions that impair intimacy, they lack a close and loving extended family, they lack support sometimes from their government, employers, and schools to live a faithful and attentive presence with spouse and children. The list goes on. It might seem that if “anti-Christianity” is so prevalent and dampening of light, a number of people just lack the means necessary to stick with a permanent, committed relationship.
That said, I think there is room to criticize the Church’s rigor. I can think of at least two situations in which popes, bishops, pajama petitioners, and canon lawyers should have little or nothing to say:
A non-Catholic in a first marriage to a divorced non-Catholic spouse (both baptized Christians) in the instance where the first person wishes to be a Catholic. In the rigorist model, the non-Catholic, non-seeking spouse must get a declaration of nullity before the seeker will be permitted to enter the Church. Even if the person was totally ignorant of Church teaching with regard to the sacramental life of divorced and remarried persons.
A Catholic who has remarried after being abandoned by a spouse. And I would interpret abandonment rather liberally: not just a physical departure from a family, but also a venture into addiction (the spouse is abandoned for the substance) or spousal abuse (where the offender has lost emotional control and perspective) and of course, adultery.
I’m not convinced there needs to be a sacramental second marriage. I’d also say that I’d tend to be a rigorist when it came to an alcoholic, adulterer, or other abuser.
I think Catholics have a right to pass around a petition like the one linked. I’m not sure it shows prudence as much as politics.
Catholic Sensibility 
Your first case seems somewhat similar to the Pauline exception in faour of the faith, with the diference between St Paul’s pagan and your baptised non-Catholic.
A more Latin concept of the law as setting guidlines which need to be interpreted pastorally would be helpful. People grow in faith and understanding and we ought to help them and not block tem with legalistic obstacles. Anyway, we are ALL sinners, none of us are really worthy of Holy Communion, so we ought to hestitate very long and hard before we dare JUDGE others as unworthy.
God Bless