Question: According to Baladeva Vidyābhūṣana, what happens to nitya-karma upon attainment of vidya (prema-bhakti)? Does it become ineffective, or does it become vidya (prema-bhakti)?
Answer: I am not sure if I understand your question. Do you mean what happens to the result of nitya-karmas performed by a devotee who attains prema-bhakti? If yes, then Baladeva explains that such a devotee does not get the outcome of his karmas. The outcome of his good karma will go to those who did service to him, who were favorable to him. The outcome of his bad karma will go to those who were critical of him.
Question: But nitya-karma, by definition, does not produce good or bad outcomes. What happens to it? Does it manifest as prema?
Answer: Don’t you think that your question is self-contradictory? If nitya-karma does not produce any apūrva, then where is the question of it manifesting as prema? Moreover, as per Gauḍīya philosophy, karma is material, and prema is the internal potency of Bhagavān. So, no karma can result in bhakti or prema. A material action cannot lead to a spiritual outcome. Prema is the mature state of bhakti, as is stated in SB 11.3.31—bhaktyā sañjātayā bhaktyā. This is the subject matter of Bhakti-rasāmrta-sindhu, second chapter, Eastern Division.
Question: Why should a Gauḍīya Vaiṣṇava perform nitya-naimittika-karma?
Answer: He does not need it in order to advance in bhakti because nitya-naimittika karmas are material and have no influence on the emergence of bhakti. He should do it to follow the social norms and not set a bad example for those who are not qualified to follow bhakti. Karma, bhakti, and jñāna are three independent paths. This is clearly stated by Śrī Kṛṣṇa to Uddhava:
yogāstrayo mayā proktā nṛṇāṁ śreyo-vidhitsayā
jñānam karma ca bhaktiśca nopāyo’nyo’sti kutracit
“For the ultimate good of people, I have spoken three types of Yoga, namely, Jñāna Yoga, Karma Yoga, and Bhakti Yoga. Besides these three, there is no other means [for the ultimate good].” (SB 11.20.6)
Bhakti is not at all dependent on karma or jñāna. You can also read the next few verses of this chapter for more clarity. Bhakti as explained in Śrīmad Bhāgavata is not understood by common people. Especially, Advaitavādis think that bhakti is a step to jñāna.
Question: Many of my relatives and friends—smartas—have become Gauḍīya Vaiṣṇavas (ISKCON) and have given up sandhyā-vandanam and the śrāddha ceremony. Hence the question.
Answer: The main reason for this is that ISKCON was founded in the USA and in its beginning state, it was primarily propagated by westerners and Indians influenced by western education. They do not have any background of nitya-naimittika-karma that includes sandhyā-vandanam. They are very much critical of any such activities. But ironically, they chant Gāyatrī three times a day. This would appear strange to any traditional Hindu. By this I mean no criticism of ISKCON and its followers. I am stating my observation to explain why your relatives have given up nitya-naimittika karmas.
Unfortunately, ISKCON does not speak very highly of smārtas. It is no wonder that your relatives have given up smārta-karma.
