robdaddyf,
my husband and I were quite involved with the NCW for about 8 months, the cathechesis class, the convivvance, preparation of the Word etc etc.
We are no longer, and briefly it is because of doctrinal challenges and what I saw as a little bit of deceptiveness.
The Mass is the Celebration of the Eucharist, for example. And we were told NOT to refer to it as Mass, because Mass implies sacrifice, and sacrifice is pagan.
Also, the “approval” that the Way talks about having is NOT canonical, but to Catholics unaware, it sounds like a nihil obstat deal…(I know that has to do with printed material, but you get the jist I hope

) meaning, the approval was for statutes aimed at correcting liturgical abuses. It is very important to understand that.
A book they gave us, “40 years of the Neocatechumenal Way/ 1968-2008 Memory”, is sort of weird. The glory seems to be given to the founders, not God.
The idea that the Church was sort of, well, pagan until Vatican II is a huge theme in their teaching, and the more I heard the more spooked I got. I loved the catechesis, loved the history, but at the end of the day, we stopped going. Mark Alessio, a great Catholic writer from CFN has a few articles you can look at. (you may be advised not to research-, another issue I had) In the end, may I recommend you read Act 5:38-39.
Lastly, Patrick Madrid, in addressing Medjugore, has a great article on his blog that you could read in deciding about the Way-different subjects but a VERY good way to look at the decisions in front of you. I highly recommend you read his article and substitute “The Way” every time you read the word Medjugore.
Of course, remember to pray

God Bless You!