Was Bishop Moises Carmona-Rivera validly consecrated?

No, in context Carmona is simply saying that some people, without any foundation at all, have claimed that he was consecrated in the new rite.  He goes on to say that others, more seriously, have claimed other things.  The implication is that any claim that he was ordained in the new rite is almost a joke.  Carmona was validly consecrated in the traditional rite.  Thus, the priest ordained through his line would be valid.  But we cannot vouch for such a priest’s doctrinal views, and there is a very strong chance that the priest denies the dogma Outside the Church There is No Salvation or supports NFP or something else.  Thus, you almost certainly couldn’t support him financially, though perhaps you could receive the sacraments from him if he is not notorious or imposing about his false views. Also, we’ve been informed that certain CMRI priests have communicated to people that they don’t want those who don’t accept baptism of desire at their chapels.  Since those CMRI priests are imposing their false views, one should not receive the sacraments from them at all.  We don’t know if this is a universal development with CMRI priests, so one should check with the CMRI priest in their area about this.  (They don’t want people who believe in that “awful” teaching that all must be baptized to be saved, as Our Lord said, but they have no problem with the idea that Jews who reject Christ can be saved.  What abominable heretics.)