ROC – from what I’m aware the majority today are either dati or masorti with a small percentage who are charedi. However I believe the masorti ones tend to be very masorti, they can still lein Torah with the temani pronunciation and such. My father in law is temani and it’s interesting to watch how they conduct the tefila in shul.
There may be a handful that are mamish chiloni and anti, but if so they are probably only the younger ones. Just like the majority of other sefardim, they were spiritually decimated when they came to Israel but even the most fargone ones are usually much more connected and traditional than their ashkenazi counterparts.