I am not a teacher. Therefore, most of what I know about them is picked up from here and there. You might want to ask teachers their opinions, and do some research, possibly through articles that may have appeared in the National Catholic Register.
The NEA as a national organization in the labor movement has backed a number of issues that are particualr to the political left and are not intrinsic to education, such as abortion. There is a feeling that they are more interested in political clout than they are in the members themselves, and that their directions do not come from the masses of teachers, but from the “politicos” who staff the national organization.