Twice in as many months (e.g., here and here), Pope Francis has inveighed against "rigid" believers. He uses very negative language against this perceived phenomenon: “They appear good because they follow the Law; but behind, there is something that does not make them good. Either they're bad, hypocrites, or they are sick. They suffer!” Such people are "enslaved," they "lead a double life." They exhibit the opposite of the beatitudes: "Rigidity is not a gift of God. Meekness is; goodness is; benevolence is; forgiveness is. But rigidity isn’t!" He attaches the same label and language to those who know, love, and respect the traditional liturgy: "Pope Francis told Father Spadaro he wonders why some young people, who were not raised with the old Latin Mass, nevertheless prefer it. 'And I ask myself: Why so much rigidity? Dig, dig, this rigidity always hides something, insecurity or even something else. Rigidity is defensive. True love is not rigid.'"
Certainly, the temptation to this sort of "pharisaical" attitude exists in the Church. It is something always to be guarded against. Because of our sacramental forms and theology, it is easy at times to get caught up in the details of the liturgy, and miss the forest (interior and spiritual realities) for the trees (exterior and physical forms, words, symbols). Likewise with the nuances of our moral theology. One can, in this sense, fall into "rigidity." And it is true that rigidity is not loving, and that rigidity resists Christ and grace.
But there is another sort of "rigidity" not often adverted to, although it appears to be far more common, currently. It consists in putting one's own will before God's, insisting that one is right while Tradition, the Church, the Bible, and God Himself must be wrong. St. James says, "Submit yourself to God... If you judge the law, you are not subject to the law." (Jms 4:7, 11). Those who are rigid in this sense judge the law of faith, and do not submit to God in their hearts.
The path of faith always involves conversion. After our initial conversion (which might be as an infant or child in Baptism), we continue to experience "ongoing conversion," as we strive over our whole life to conform our hearts and minds, our loves and desires, to those of Christ. To be united with Christ in this conformity, "putting on the mind of Christ" (Rom 2:12, etc), is precisely what it means to live as a Christian.
The heart experiencing conversion must be humble. It must recognize and accept (even when there is struggle actually to do - concupiscence is a real thing) that what the believer desires, of himself, is likely not what God desires for him, and therefore that one must learn to desire instead what God desires. This softness and pliability of the heart in respect to God's Law, Revelation, commandments and precepts, personal vocation, moral law, and Tradition is properly understood as a sign of strong faith. As the Rule of St. Benedict says in its very first words, "Listen carefully, my son, to the Master's instructions, and attend to them with the ear of your heart... The labor of obedience will bring you back to Him from whom you have drifted by the sloth of disobedience." This is the opposite of rigidity. (See e.g. the parable of the Pharisee and the publican, Lk 18:9-14.)
Rigidity, then, is not only clinging to the exterior forms of religion, which Pope Francis (rightly) decries. The willful rejection of Tradition is equally a form of rigidity (see e.g. Dei Verbum #7-8, etc). It is a hardness of heart with respect to God's calling the believer. It is spiritual pride, asserting in effect that this generation (or even this individual!) knows better what is good for souls than all prior generations, than all prior saints, doctors, mystics of the Church. I don't think it's too strong to say that there's more than a touch of idolatry, of self-worship, in this attitude. (It remains true that much of the rejection and loss of Tradition and faith in the last century is not willful, but from ignorance and weakness.)
Thus, one might correctly say: The idea that external or physical forms (e.g., the construction of a church, the placement of the Tabernacle, the beauty of vestments and statues, etc) don't matter to internal or spiritual realities (faith, union with God, repentance and conversion) is false (e.g. Sacrosanctum Concilium #8, 112-3, 122-5, etc). To cling to this idea in the face of Tradition and correction is to be rigid.
Idem: The idea that Christ did not and does not will the seven Sacraments for the Church, as the primary means of salvific grace for believers, is false (e.g. SC #5-8, Lumen Gentium #7, 11, etc). To cling stubbornly to the opposite idea, that we can meddle with the Sacraments or deny their efficacy, in the face of Tradition and correction, is to be rigid.
Idem: The ideas of moral relativism and religious indifferentism are false (e.g. Dominus Iesus, Fides et Ratio, etc). To insist, in the face of Tradition and correction, that they are true, is to be rigid.
And so forth.... In short, modernism is rigid, but Tradition properly received and loved ("the living faith of the dead," as one great Church historian noted) is life with Christ.