On the Catholicism series:
It's difficult to understand why Bp. Robert Barron's efforts would be described as a "faith-formation series." The Catholicism series is, without question, a celebration of Catholic art and history and, to a degree, an education in "what Catholics believe and why." There are a number of commendable points in the series. But Barron's overall approach seems to lack any sense of urgency about whether one ought to be Catholic at all. In that sense, the series is very "ecumenical" and unlikely to move anyone who is not already Catholic to consider entering the Catholic Church. This "ecumenical" sense is reinforced by the numerous references to non-Catholic (even non-Christian) philosophers and thinkers, much as we saw in the YouCat catechism. There is nothing here to challenge an unbeliever, but quite a bit to reinforce one who already believes. The word "Catholic" seldom appears within individual episodes themselves. It is also surprising to hear how often Barron refers to "Jesus' message of non-violence."
We don't recommend Catholicism as a faith formation series. It is certainly educational, and the visual insights into what the Catholic faith has inspired over the centuries are, indeed, stunning. But the series isn't evangelization in any meaningful sense. Unbelievers may come away more enlightened and more informed, believers may come away confirmed in their belief, but no one is likely to be moved to conversion, as the message that conversion to the Catholic faith is necessary for salvation is nowhere present in the series. The Catholic faith did, obviously, inspire magnificent art, architecture, literature and music. Jesus was of course a great teacher with moral insights that are universally applicable. It just isn't obvious, in Barron's approach, that Jesus was necessarily God who established One True Church on earth. There isn't much here to explain why people would be willing to suffer martyrdom for the Faith.
For a more thorough review of Bp. Barron's series Catholicism, click on this link.
On the claim that "There's a reasonable hope that Hell is empty":
Bishop Barron articulates his views on Hell in two YouTube videos here and here. Although his views on this subject may be expressed with more nuance elsewhere, he is widely understood to hold that there is a realistic hope that Hell is empty. That this accurately represents his point of view is supported by his vigorous disagreement with Dr. Ralph Martin in his book Will Many Be Saved? (see also Dr. Martin's response to Fr. Barron and his May 28, 2015 appearance On EWTN).
Others understand Barron as we do:
A number of saints, Doctors of the Church, Scripture and Our Lord Himself also speak clearly against the theory that there's a reasonable hope Hell is empty of human souls.
Bishop Barron may say and do many commendable things but it's possible to be wrong on something so fundamental that it casts a shadow over everything else. It is, of course, necessary to live and pray with the hope that we ourselves and every other person will be responsive to the grace of God that will lead them to salvation which is offered to all men. We cannot know the final judgment of any individual person, living or dead, but when Our Lord gives clear witness to the reality that not all men will be saved, then it is folly to maintain that it is reasonable to hope that all men will be saved. If all men will not be saved, then one cannot reasonably hope for what is known to be false and impossible. If Barron concedes that Hell exists (as he does) and that there will be people (human beings) who go there (which it seems he does), then he cannot continue to say it is reasonable to hope no human being is in Hell. There's just no other way to look at this.
We would be happy to issue a clarification on this if we had any reason to believe we are wrong in our judgment of Barron's theological opinion on Hell (which does not, in fact, agree with any Pope). It is not reasonable to hope that all men will be saved because Our Lord Himself said that all men will not.
Ideas have consequences. Affirming the possibility that all men will be saved flies in the face of the words of Our Lord Himself. It may be possible to argue that Our Lord merely issued hypothetical warnings, but then what was the point of His life and death if there was nothing but a philosophical hypothesis from which we needed to be saved? Prior to Our Lord's sacrificial death, there was no possibility of Heaven for anyone. After His death, Heaven became possible for everyone — but many will not accept the grace necessary to achieve this end. All men can choose Heaven, but not all men will. That being so, it is not reasonable to affirm that Hell may be empty. We may not know that any specific person is in Hell, but we must accept that there are human beings, possibly many human beings, who will go there. Our Lord said so!
Why should anyone be Catholic, or even virtuous, if it is reasonable to affirm that no one goes to Hell anyway? Our Lord talks about Hell more than any other topic outside His divinity. Why do that if it is little more than a scary hypothesis? A case could be made that Our Lord spent a good deal of time scaring people with false and manipulative statements if Barron is correct. No one is denying that God's mercy is available to everyone, but there are no examples in the Gospels of anyone being shown mercy without some sign of repentance. Barron makes Divine Mercy sound like cheap grace, and in doing so, gives people little reason to repent of anything. If the consequences are the same whether one shows contrition and repentance or not, why bother? Why go to confession? Why acknowledge our sins?