Damian Thompson has mentioned the possible full reconciliation of the curiously-named traditionalist Transalpine Redemptorists with the Holy See. I visited their blog to find out more, and found this most interesting (if a little long) account by their superior, Fr Michael Mary, about his attitude to this question.
I have been reading their regular newspaper, Catholic, for some years now, and have found it really quite edifying. It would be a genuine joy to be able to have no reservations at all about their work.
They have members following a number of different rites who, as you'll see on the accompanying YouTube video, wear a curious variety of headgear.
They have wandered quite a lot over the years; I seem to remember them being in Guildford when I was a seminarian nearby, at the SSPX Mass centre run by the formidable Miss Hobbs (who I seem to remember was a childhood friend of Charles de Gaulle). I used occasionally to attend Mass there, until the Episcopal consecrations put me off the idea. Then, I think, the community moved to the Isle of Sheppey, a bleak spot at the best of times. That not being bleak enough, they moved to their present home on Papa Stronsay, in the Orkneys. This establishment looks very permanent; they are in the process of building a substantial monastery which has already attracted quite a lot of attention, and from this remote spot carry out quite an apostolate.
Which is to say, it would be very encouraging to have them fully on board, as it were.