How did I miss this?
The Pope spoke about those who "'use rigidity in order to cover over weakness, sin, personality problems; and they use rigidity' to build themselves up at the expense of others
It is very true. The Pope is right. There are those who do that. In fact, been there, done that.
Not necessarily intentionally - to expressly live a double life - but I did. I know others who have done so, or still do so. People like that know the rules and make sure others know them too, albeit careful to hide, and/or deny their own slip-ups, often doubling down even more rigidly upon themselves - and others - after every fall. The dishonesty is often not seen because the rigid decorum, or the severe preachiness of their attitude, distracts them from their real sin. Sometimes their big sins distract these types from their root sins. It may be an affection for a particular sin, and they try to purge its effects by rigidity - believing it their one and only sin. As the Pope points out, some of these, like Saul, are 'sincere' but rigid.
God doesn't give up on us.
I am sure this was what Pope John Paul the First meant when he spoke about why our Lord sometimes permits mortal sin:
"I will limit myself to recommending one virtue so dear to the Lord: He said, 'Learn from me who am meek and humble of heart." I risk saying an error, but I am saying it: the Lord loves humility so much that, sometimes, he permits grave sins. Why? So that those who have committed these sins, afterwards, having repented, may remain humble. One is not tempted to believe oneself half–saint or half–angel, when one knows that one has committed grave faults. The Lord so much recommended: be humble." John Paul I
Then there are rigid people living a double life ...
This is hard for me to explain but I know it from experience. Pope Francis is very candid about it, very frank, because he must have witnessed it over and over in the priests, religious and laity he directed over the years. He knows. His homilies are precious for opening our eyes to our own hypocrisy, helping us to see the log in our eye which prevents us from seeing our own sins and faults. The rigid are convinced of their righteousness and look down on the sins of others - even though they say they love the sinner but hate the sin.
Speaking of Saul from today's first reading, the Holy Father explains:
“They are rigid people living a double life: They make themselves look good, sincere, but when no one sees them, they do ugly things. On the other hand, this young man was honest. He believed that. I think, when I say this, of the many young people in the Church today who have fallen into the temptation of rigidity. Some are sincere, they are good. We have to pray that the Lord might help them to grow along the path of meekness.”
It is so clear that the Holy Father is not condemning anyone - and especially not the sincere, but rather warning them against the trap of rigidity and hypocrisy.
I have known priests and religious and laity who were/are very orthodox - some very rigid indeed. When they wanted to be, they could be indulgent, even sparing in their judgement - travelling to the ends of the earth, so to speak, to make one convert only to turn them into something worse than themselves. Some of these types are in, or have been put in jail. One priest I know killed himself. Others left religious life, and some just retreated more deeply into some sort of ritual horarium. I recall one really very strict priest who was arrested at a gay cruising site - he's the type the Holy Father speaks of.
To be sure, everyone who keeps the commandments and loves tradition and lives a devout life is not rigid. Carthusians and Discalced Carmelite Nuns, though living a very strict life, are not rigid. They can't be - because they will break. However, in the end, even if they break, that too is a grace, since they are able to repent, to become meek and humble.
The Pope is not condemning people, but calling us to conversion. He knows what it is to be rigid and closed ...
“This is the path of the Christian: to go forward along the path marked out by Jesus: the path of preaching, the path of suffering, the path of the Cross, the path of the resurrection. Today, in a special way, let us pray to Saul for those in the Church who are rigid: for the rigid who are sincere, as he was, who have zeal, but are mistaken. And for the rigid who are hypocrites, those who live a double life, those of whom Jesus said, ‘Do what they say, but not what they do.’ Let us pray today for the rigid.” - Source
In conclusion, if we stand accused, there is something else from Pope John Paul I to give us hope:
[...]No human sin —however serious—can prevail over or limit mercy. After serving for several years as the Bishop of Vittorio Veneto, Albino Luciani held some training exercises for parish priests, and when commenting on the parable of the Prodigal Son once said this about the Father: “He waits. Always. And it is never too late. That’s what he’s like, that’s how he is . . . he’s a father. A father waiting at the doorway, who sees us when we are still far off, who is moved, and who comes running toward us, embraces us, and kisses us tenderly . . . Our sin is like a jewel that we present to him to obtain the consolation of forgiveness . . . Giving a gift of jewels is a noble thing to do, and it is not a defeat but a joyous victory to let God win!””