When I was in the process of becoming Catholic, a significant conversional moment occurred when I had dinner with an Opus Dei priest, who arrived in full Roman habit, impressing me mightily.
This article from the EWTN Library examines why it is so crucial for priests to wear their traditional priestly attire.
“In a secularized and tendentiously materialistic society, where even the external signs of sacred and supernatural realities tend to be disappearing, the necessity is particularly felt that the priest-man of God, dispenser of His mysteries-should be recognizable in the sight of the community, even through the clothing he wears, as an unmistakable sign of his dedication and of his identity as a recipient of a public ministry. The priest should be recognizable above all through his behavior, but also through his dressing in a way that renders immediately perceptible to all the faithful, even to all men, his identity and his belonging to God and to the Church.
“For this reason, the cleric should wear "suitable clerical clothing, according to the norms issued by the Episcopal Conference and according to legitimate local customs." (Canon 284) This means that such clothing, when it is not the cassock, should be distinct from the manner in which laymen dress, and in conformity with the dignity and sacredness of the ministry.
“Apart from entirely exceptional circumstances, the non-use of clerical clothing on the part of the cleric can manifest a weak sense of his own identity as a pastor completely dedicated to the service of the Church (# 66).
“Given this timely reminder from the Holy See about the importance of clerical attire for the priest, we thought it might be useful to examine some of the underlying reasons for this discipline. We also want to examine some of the common arguments used to justify the non-wearing of the Roman collar.
“It is our contention that the rather widespread practice of priests neglecting to wear their collar when they should is both a sign and a cause of malaise in the Church. Such casualness about being publicly identified as a priest of the Catholic Church may signify a desire to distance himself from his priestly vocation. The collar becomes "work clothes," which are put away when one is not "on duty." The functionalistic notion of the priesthood revealed by this attitude is in contradiction to the ontological configuration to Christ the High Priest conferred by priestly ordination.
“Lay people depend on their priests for spiritual support and strength. They feel that something is not right when their priests try to blend into the crowd and, as it were, disappear.
“The purpose of this article is to encourage our fellow priests to wear their collars (and, by analogy, religious to wear their habits).
“It goes without saying that there are reasonable and legitimate exceptions to this rule, such as during sports and recreation, during one's vacation (in general), while at home with family or in one's private quarters in the rectory. And, of course, the obligation to wear clerical clothing ceases during times of violent persecution.
“During such a crisis, the guidance of the bishops should be followed.”