Not sure about discouraged, but there were many clergy faculty members when I was at university in the UK. I observed that Dominicans and Jesuits wore jacket and tie for teaching, Benedictines and Franciscans wore the habit. I know a Benedictine who wears secular clothes to travel in order not to look ostentatiously monastic. I’ve met a Rosminian priest who is also a professor, and he wears a jacket and tie, often a dark suit with white shirt and a white tie. In the university context, I’ve known Anglicans and Baptists who also wore secular clothes more or less all the time.
I’ve known clergy who wear secular clothes when semi off-duty, e.g. taking kids from the choir to a theme park.
I’ve also known clergy to wear secular clothes where they think it may be more sensitive to the occasion, mostly when meeting someone who is a survivor of clergy/religious abuse, for whom meeting somebody wearing a clerical collar would be potentially distressing or even, as people now say, triggering.
Oh, also, when attending a wedding or funeral at which they have no official role, in order not to upstage the minister, so to speak.
I am not a priest, obviously. These are my observations though.