There is always a difference of opinion between a smārta-brāhmaṇa and a Vaiṣṇava gosvāmī. There are even smārta opinions and Vaiṣṇava gosvāmī opinions available in astrological and astronomical calculations. By calling Nityānanda Prabhu a bhraṣṭa avadhūta (a rejected paramahaṁsa), Advaita Ācārya Prabhu in a sense accepted Nityānanda Prabhu as a paramahaṁsa. In other words, Nityānanda Prabhu had nothing to do with the rules governing smārta-brāhmaṇas. Thus under pretense of condemning Him, Advaita Ācārya was actually praising Him. In the avadhūta stage, the paramahaṁsa stage, which is the supermost stage, one may appear to be viṣayī, on the platform of sense gratification, but in actuality he has nothing to do with sense gratification. At that stage, a person sometimes accepts the symptoms and dress of a sannyāsī and sometimes does not. Sometimes he dresses like a householder. We should know, however, that these are all joking words between Advaita Ācārya and Nityānanda Prabhu. They are not to be taken as insults.
In Khaḍadaha, sometimes people misunderstood Nityānanda Prabhu to belong to the śākta-sampradāya, whose philosophy is antaḥ śāktaḥ bahiḥ śaivaḥ sabhāyāṁ vaiṣṇavo mataḥ. According to the śākta-sampradāya, a person called kaulāvadhūta thinks materially while externally appearing to be a great devotee of Lord Śiva. When such a person is in an assembly of Vaiṣṇavas, he appears like a Vaiṣṇava. Actually Nityānanda Prabhu did not belong to such a community. Nityānanda Prabhu was always a brahmacārī of a sannyāsī of the vaidika order. Actually He was a paramahaṁsa. Sometimes He is accepted to be a disciple of Lakṣmīpati Tīrtha. If He is so accepted, Nityānanda Prabhu belonged to the Madhva-sampradāya. He did not belong to the tāntrika-sampradāya of Bengal.
Ref >> Srila Prabhupada Vani.