One of the thoughts floating in the Krishna consciousness movement is that an education centered around Sanskrit and Vedas is not a necessity in the Krishna consciousness movement. There are also thoughts that Vedas deviate one from pure devotion. The verse often cited in this regard is:

trai-guëya-viñayä vedä

nistrai-guëyo bhavärjuna

nirdvandvo nitya-sattva-stho

niryoga-kñema ätmavän

The Vedas deal mainly with the subject of the three modes of material nature. O Arjuna, become transcendental to these three modes. Be free from all dualities and from all anxieties for gain and safety, and be established in the Self. (BG 2.45)

Vedas have three different branches namely Bramhana, Aranyaka and Upanishads. Prabhupada has regularly quoted in his purports from the Mundakopanishad, Kathopanishad, Shwetashwara Upanishad etc. Prabhupada has even translated the Ispoanisad. All these are parts of different Vedas. Bramhana and Aranyaka part of the Vedas guide about the rituals and the Upanishad gives direct spiritual knowledge. So shoud we study only the Upanishad section of the Vedas and leave the other sections? This is what Shankaracharya did and so Madhwacharya has criticized the same. Others like Shabara have given commentary only on bramhana and aranyaka. But Krishna says in the Bhagavad Gita:

1) In all vedic literature beginning from four vedas, vedanta sutras, Upanishads and Puranas the glories of the Supreme Lord are celebrated. By performance of Vedic rituals, discussion of Vedic philosophy, and worship of Lord in devotional service He is attained.

(BG 15.18)

2) The vedas give the right direction to people so that they can mould their lives and come back to Godhead, back to home. The Vedas offer knowledge of the Supreme Personality of Godhead Krishna, and Krishna in His incarnation as Vyasadeva is the compiler of the Vedanta Sutras.

(BG 15.15 purport)

3) That best of brähmaëas, the spiritual master Sändépani, was satisfied with Their submissive behavior, and thus he taught Them the entire Vedas, together with their six corollaries and the Upaniñads (SB 10.45.33)

4) One has to study the Vedas under the guidance of the spiritual master and undergo many austerities and penances while living under his care. A brahmacäré has to live in the home of the spiritual master just like a servant, and he must beg alms from door to door and bring them to the spiritual master. He takes food only under the master's order, and if the master neglects to call the student for food that day, the student fasts. … After the student studies the Vedas under the master for a period from five to twenty years, he may become a man of perfect character. Study of the Vedas is not meant for the recreation of armchair speculators, but for the formation of character. After this training, the brahmacäré is allowed to enter into household life and marry. (Bhagavad-gétä As It Is, 8.28 purport)

5) The institution of varëa and äçrama prescribes many regulative duties to be observed by its followers. Such duties enjoin that a candidate willing to study the Vedas must approach a bona fide spiritual master and request acceptance as his disciple. The sacred thread is the sign of those who are competent to study the Vedas from the äcärya, or the bona fide spiritual master. (SB 1.1.2)

6) "Bhakti-sastri'' is awarded after extensive study of Bhagavad-gétä, Easy Journey, and Nectar of Devotion. "Bhakti-vaibhava'' is awarded after study of Vedanta-sutra and Srimad-Bhagavatam on a preliminary basis; and "Bhaktivedanta'' the highest title, is awarded after extensive study of Caitanya-caritamrta. (Letter to Bramhananda, 23 Mar 1969)

Vedas and Vedanta are traditional subjects of knowledge. Srila Prabhupada also has put sufficient emphasis in his books on the need to study these. On the contrary there doesn’t seem to be any explicit quote on the problems with the study of Vedas and Vedanta. Prabhupada mentions in the Chaitanya Charitamrita

Taking advantage of these verses, there are some sahajiyās who, taking everything very cheaply, consider themselves elevated Vaiṣṇavas but do not care even to touch the Vedānta-sūtra or Vedānta philosophy. A real Vaiṣṇava should, however, study Vedānta philosophy, but if after studying Vedānta one does not adopt the chanting of the holy name of the Lord, he is no better than a Māyāvādī.

CC Adi 7.72, Translation and Purport

Hence Prabhupada is agreeing with the traditional way of knowledge by emphasizing the need for Vedas and Vedanta. Vedas provide the necessary culture in human society and Vedanta helps in having a solid philosophical basis for devotees. As explained earlier, this knowledge begins at an early age when the disciple is in a gurukula. Hence there is a need to revive this traditional education and gurukulas are a good ground for this.