Be careful of what you mean by traditional. If we mean by the term, rooted in 1500 years of Church Tradition, then yes. But what most people in the Traditional forum think of the term could not be applied to many monastic communites.
The Mass at many Benedictine abbey Churches are celebrated in the vernacular with the community gathered around a free standing altar. Many monastic communites welcome all denominations and faiths and the extent to which they do so would offend most self labeled “Traditionalists”. I know a monk who is good friends with some Buddhist monks and has prayed with them. Some of the monastic communites concern with care of the poor, violence and war would challenge the sensibilities of many “Traditionalists”.
I think this is one small part of the reason why I am attracted to Benedictine monasticism, especially Cistercian/Trappist, because they challenge commonly held views of many people including myself. They force you to think outside of yourself and what you were brought up to believe and think. Christ was like that with his disciples, challenging them to accept new ways of thinking which were considered radical in his day.
-Tim-