There are, I know, some Traditionalists who feel uneasy about any priest who ever celebrates the Novus Ordo. They acknowledge that the Novus Ordo Mass is valid; but they feel so strongly about its inadequacies that they could never attend an Old Rite Masss celebrated by a priest who had 'compromised' himself in this way; they see a question mark hanging over the ministry of any priest who feels able to celebrate so flawed (as they see it) a rite.
I do not think that this attitude quite does justice to the complexities of the situation. For example: the Dominican Rite has differences from the Tridentine Rite ... a different Confiteor, different (and much shorter) Offertory Prayers ... So: if a priest celebrated the Novus Ordo in Latin and versus Orientem, selecting of course the Roman Canon, how could such a celebration be seen as more radically different from the Tridentine Rite than the Dominican or Carmelite Rites are? And would such 'strict' lay people refuse to attend a Sarum Mass, used in Medieval England and in the English Seminaries abroad until Dr Lawrence Webb arrived from Rome in December 1576 and began to teach the new Missal? Not to mention, of course, the (old) Ambrosian Rite, with its archaic positioning of the Fraction. Bishop Fellay is reported to have spoken favourably of a thoroughly traditional celebration of the Novus Ordo; and let it be remembered that Archbishop Lefebvre adopted the incremental changes made in the Ordo Missae throughout the 1960s, only returning to the Classical Roman Ordo Missae, with the Iudica me and the Last Gospel et cetera, in the mid 1970s.
But I think there is a more radical personal consideration than that. This is what I think gets to the heart of the matter: does a priest think of the Old Rite as the Gold Standard? Does he naturally, automatically, instinctively, say his own private Mass, when pastoral considerations do not require of him a public Mass, in the Extraordinary Form? Is his spirituality formed by the Old Rite? Does he do the Novus Ordo in as traditional a way as pastoral circumstances allow him? Is his whole attitude, and his ritual care about such things as reverence for the Blessed Sacrament, formed by his grounding in the Old Rite? Perhaps is he a priest, brought up on the Novus Ordo but knowing better, and who is doing his best to learn and understand the Old Rite? Perhaps he is an Ordinariate priest, nurtured by the devout and sacramentally orthodox and orthopraxic culture of Anglo-Catholic worship and now employing the vernacular but orthodox and most laudable liturgy to be found in the Ordinariate Missal?
Such priests are quite different from a cleric who celebrates the Novus Ordo without a care or a thought, and whose instincts and, indeed, prejudices are lodged firmly in the tawdry world of the 1970s monoculture; even if he may have learned the Old Mass so as to be able occasionally to say it in order to keep some silly old (or young) people quiet.
Of course, things being as they are, there will be clergy who are somewhere in between. My concern is to make very clear my view that a generosity of approach on the part of laity and clergy is very much more rational and desirable than a harsh rigidity.
If God had wanted you to live your Catholic life in the 1930s, that is where he would have put you!