One point of controversy that often comes up in relation to the classical form of the Roman Rite is that of the responses. The usual practice was for the server (or the Deacon and Subdeacon at High Mass) to make the responses on behalf of the people. The "Dialogue Mass" was introduced under Pope Pius XII whereby everyone could "join in" with the responses.
Nowadays, when the older form of the Roman rite is used, aficionados get annoyed if people join in with the responses. People who are used to the newer form of Mass get annoyed and say that it is ridiculous that we cannot join in with the "Our Father", for example
One source of the problem was the rather dictatorial way in which the English responses were introduced in the early 70s. People were cajoled and hectored because they didn't say "And also with you" loudly enough. In some places it became a pantomime: "The Lord be with you... I can't HEAR you ... The LORD be WITH you..." and so on. The result is that people feel that they are somehow participating better if they shout out the responses as loudly as they can.
It seems to me that a good compromise when re-introducing the older form of the Mass would be to accept it if people want to join in with "Et cum spiritu tuo" or "Amen" at various points but to encourage them do so in a reasonably quiet voice to allow the server to lead the responses. At the same time, it can be made clear (to the relief of many) that people can be quiet and say their own prayers in union with the priest if they want to.
When celebrating Mass in Latin, the older form is more pastorally suitable than the newer form in that it is natural for the server to take up the more complex responses on behalf of the people. With the newer rite, people have to either read from a book or learn the Latin Confiteor and the Suscipiat by heart. For some people that is fine - for others it is indeed a "barrier to participation" if such a chorus is seen as being of the essence of real participation.
Of course the real participation called for by the Liturgical Movement and by Vatican II is primarily concerned with uniting ourselves spiritually with the Divine Victim. For some people this can be reinforced externally by joining in quietly with the responses. For others it is fine to pray quietly, uniting the mind and heart in a contemplative spirit with the Liturgical Action that is taking place at the altar.
With the older form of the rite, a wider range of external participation is possible. With the newer rite, it seems to me that only one sort of participation is allowed - that of joining in audibly with the responses, reading things in a book or listening attentively to today's passage from the book of Numbers.