Advaita and ISKCON

Firstly I must say neither Srila Prabhupada nor any of the ISKCON devotees or any of the Four Vaishnava Sampradayas (Sri,Brahma,Rudra,Kumara -  Srila Prabhupada is the 32nd Acharya in the Brahma-Madhva-Gaudiya Sampradaya) have anything against Sripada Shankaracharya. He is a spiritual master and he is the incarnation of Lord Shiva who I suppose has been described very nicely by Deepesh Baghel. In fact we are extremely obliged to him because of his mercy only atheism has departed and Vedic Principles were restored to its original glory after Lord Buddha's advent.

Sri Chaitanya Mahaprabhu confirms that Sri Sankara is only following Lord Vishnu's order(Quoted from Sri Chaitanya Charitamrita Adi Lila 7.110:

Lord Shiva is explicitly ordered by Lord Vishnu as you will see in the below verses I quote to promote the philosophy(i.e. Advaita Vedanta) for a very specific and special purpose.

TRANSLATION
“[Addressing Lord Siva, the Supreme Personality of Godhead said:] ‘Please make the general populace averse to Me by imagining your own interpretation of the Vedas. Also, cover Me in such a way that people will take more interest in advancing material civilization just to propagate a population bereft of spiritual knowledge.’

- Padma Purana, Uttara-khanda (62.31).

Actual Reference: PadmaPuran, Uttara Khanda, 71 Chapter 107th Verse 


Also, in the Varaha Purana Lord Visnu instructs Siva saying:

esa moham srjamy asu yo janan mohayisyati
tvam ca rudra maha-baho moha-sastrani karaya

O mighty-armed Siva, please write books filled with lies, and thus bewilder the people.

atathyani vitathyani darsayasva maha-bhuja
prakasam kuru catmanam aprakasam ca mam kuru

O mighty-armed one, please preach a collection of lies. Place yourself in the
forefront,and conceal Me.

[Lord Vishnu addresses  Lord Shiva]: “In Kali-yuga, mislead the people in general by propounding imaginary meanings for the Vedas to bewilder them.”

- Shiva Purana

The only problem is the philosophy is not suitable for God-realization and will mislead one.

Issue One : Misinterpretation of Vedic Literature - Mukhya Vritti vs Gauna Vritti

Now naturally comes a question why did he do so. I quote from Padma Purana where Lord Shiva explains the entire scene to Mother Parvati:

“The Mayavada philosophy,” Lord Shiva informed his wife Parvati, “is impious [asac chastra]. It is covered Buddhism. My dear Parvati, in Kali-yuga I assume the form of a brahmana and teach this imagined Mayavada philosophy. In order to cheat the atheists, I describe the Supreme Personality of Godhead to be without form and without qualities. Similarly, in explaining Vedanta I describe the same Mayavada philosophy in order to mislead the entire population toward atheism by denying the personal form of the Lord.”

The recommendation by Vedic Literatures that they be understood without any misinterpretation otherwise it's of no use. Henceforth I quote Srila Madhvacharya, who commenting on the aphorism drishyate tu (Vedanta-sutra 2.1.6), quotes the Bhavishya Purana as follows:

The Rg Veda, Yajur Veda, Sama Veda, Atharva Veda, Mahabharata, Pancharatra and original Ramayana are all considered Vedic literature. The Puranas  are especially meant for Vaishnavas and are also Vedic literature. As such, whatever is stated within the Puranas, Mahabharata and Ramayana is self-evident. There is no need for interpretation. The Bhagavad-gita is also within the Mahabharata; therefore all the statements of the Bhagavad-gita are self-evident.There is no need for interpretation, and if we do interpret, the entire authority of the Vedic literature is lost.

The issue is technically known as the Mukhya-vrtti and Gauna-vrtti issue which is explained here by Srila Prabhupada in Sri Chaitanya Charitamrita Adi Lila 7.110 Purport:

Srila Bhaktisiddhanta Sarasvati Thakura comments that mukhya-vritti (“the direct meaning”) is abhidhaa-vritti, or the meaning that one can understand immediately from the statements of dictionaries (namely Nirukti), whereas gauna-vritti (“the indirect meaning”) is a meaning that one imagines without consulting the dictionary. For example, one politician has said that Kurukshetra refers to the body, but in the dictionary there is no such definition. Therefore this imaginary meaning is gauna-vritti, whereas the direct meaning found in the dictionary is mukhya-vritti or abhidha-vritti. This is the distinction between the two. Sri Caitanya Mahäprabhu recommends that one understand the Vedic literature in terms of abhidhaa-vritti, and the gauna-vritti He rejects. Sometimes, however, as a matter of necessity, the Vedic literature is described in terms of the lakshanaa-vritti or gauna-vritti, but one should not accept such explanations as permanent truths.

Issue Two : Narayana and the living entities are on the same platform

Lord Shiva explains this in His conversation with Mother Parvati in the continuation from the above verses :

“My dear wife, hear my explanations of how I have spread ignorance through Mayavada philosophy.Simply by hearing it, even an advanced scholar will fall down. In this philosophy, which is certainly very inauspicious for people in general, I have misrepresented the real meaning of the Vedas and recommended that one give up all activities in order to achieve freedom from karma. In this Mayavada philosophy I have described the jivatma and Paramatma to be one and the same.”

And the above is the greatest blasphemy to compare an ordinary soul to the Supreme Personality of Godhead, Lord Narayana. The demigods themselves cannot be compared to Him what to speak of ordinary souls:

A person who considers demigods like Brahma and Shiva to be on an equal level with Narayana is to be considered an offender and an atheist.

Also stated in the Padma Purana (Brahma-khanda 25.15), in the description of the ten offenses against Lord Vishnu’s holy names, we read :

To think the names of demigods such as Lord give to be as good as the name of Lord Vishnu—or in other words, to think Lord Shiva and the other demigods to be other forms of God and therefore equal to Vishnu—is also blasphemous.

I suppose it has been sufficiently explained. But you can understand it better if you read Teachings of Lord Chaitanya by His Divince Grace Srila Prabhupada and especially the Conversation series with Srila Prakashananda Saraswati and Srila Sarvabhauma Bhattacharya.

And Sripada Shankaracharya already declares Lord Krishna as the Supreme Personality of Godhead in Gita-Mahatmya:

In this present day, people are very much eager to have one scripture, one God, one religion, and one occupation. Therefore, ekam sastram devaki-putra-gitam: let there be one scripture only, one common scripture for the whole world-Bhagavad-gita. Eko devo devaki-putra eva: let there be one God for the whole world-Sri Krishna. Eko mantras tasya nämäni: and one hymn, one mantra, one prayer—the chanting of His name: Hare Krishna, Hare Krishna, Krishna Krishna, Hare Hare/ Hare Rama, Hare Rama, Rama Rama, Hare Hare. Karmapy ekam tasya devasya seva: and let there be one work only—the service of the Supreme Personality of Godhead.

And as far as Bhaja Govindam is concerned, that is Shankarachrya's final ultimatum to those who are wrangling with grammar and logic and not coming to the ultimate conclusion of the Vedic Literatures - devotion to Lord Sri Krishna :

Srila Prabhupada explains :

This is Sankara's last instruction to his followers, and the purport is that the mayavadi philosophers are very much accustomed to draw favorable meanings from unwanted interpretations by grammatical jugglery. In Sanskrit the grammatical jugglery is a great puzzle, there are many words which can be changed into different meanings by grammatical root derivations and affixing and prefixing pratyayas. So Sankara advised that do not try to exact favorable conclusions by beating the Sastras, but be submissive to Lord Govinda and worship Him. Otherwise, this grammatical jugglery of words will not help you at the time of death. At that time only if you can someway or other remember the Lotus Feet of Govinda, Krishna, that will save you, O' the fool number-one. Don't waste your time in misinterpreting scriptures.

Srila Prabupada's letter to Jayapataka, Los Angeles 21st January, 1970

ref: https://www.quora.com/I-know-Iskcon-and-Srila-Prabhupada-do-not-have-anything-positive-to-say-about-Advaita-of-Adi-Shankara-What-do-they-think-of-Adi-Sankaras-hymn-Bhaja-Govindam