“They” are the teaching authority of the Church, entrusted with the deposit of faith which was handed down by the apostles. I suppose it is possible that the Father and the Holy Spirit could have become incarnate, but the fact is that they didn’t. If the Church says as much, it’s not limiting the power of God, it’s simply declaring the truth of what is. It’s not limiting God if we don’t sign off on a hypothetical. Asking “who are they” to call something heresy is like asking “who is the referee to tell me how to play football?” The referee has a job, namely to make sure the game stays within the bounds of what’s been handed down as football. If we fail to follow the laws of the game, we aren’t really playing football. And if we go outside of the bounds of what has been revealed by Christ to the apostles and handed down by them, then it is not really the truth that we believe. The magisterium of the Church exists to safeguard what is handed on as true, not to make up new things or pass on their own opinions.
Notice too that the language with which the Incarnation is described is never that of necessity, what God had to do (as this would place limits on his sovereign will), but rather the language of what was most fitting.
-Fr ACEGC