Such criticisms were muted during Wolsey’s rule. Most anticlericalism dates from the 1530s and later, when the Protestant reformers sought to justify their destruction of the Catholic Church.
The English Church in the 1520s was well respected and highly regarded.
The control of the Church by the king is known as Erastianism. The English Church was an Erastian Church.
Ultimately, the king, not Wolsey, ran the Church. The king made all the appointments and rewarded churchmen as he saw fit. He employed them extensively on government business. The king, after all created Wolsey.
The bishops at this time were able and worthy men, who served the king and the Church. Bishop Fisher was particularly respected when he opposed the king’s campaign to annul his marriage.
Wolsey’s career illustrates the fact that the Church represented the only way for talented commoners to rise to positions of power and influence