Religious orders have their own regulations and formation processes, their own discipline systems...It is useful at this point to remember that the only order in the two-thousand-year history of the Church that has not required reform at some point is the Carthusians...Monastic orders have historically had their share of problems, but they tend to eliminate many of these problems by intentionally limiting contact wit the secular world. These orders do not seek out secular formation. Religious teaching orders have not this luxury.
In effect, with the formation of the compulsory parochial school system, the bishops had created a double-edged sword. The system would not only allow doctrine to be efficiently disseminated, it would also allow heresy to sweep unchecked through their flocks if, or more likely when, the religious teaching orders became heterodox. Furthermore, these religious taught children, that segment of the population that is least able to resist the blandishments of error and heresy.
I am somewhat sympathetic to Kellmeyer's diagnosis. Yet the collapse of catechesis in Western countries seems to have been too widespread to have been the fault of religious orders. Surely some orders would have been more resistant to heresy than others.
Further, many of the problems in religious education are due not to theological error but lax, content-free educational styles. Though indifferentism is technically a heresy, indifference is also a vicious habit undermining quality education.