Even those who take advantage of karma-kanda and jnana-kanda, but are not at least slightly devoted cannot be purified simply by following these other paths
SB Canto 6
My dear King, as a pot containing liquor cannot be purified even if washed in the waters of many rivers, nondevotees cannot be purified by processes of atonement even if they perform them very well.
To take advantage of the methods of atonement, one must be at least somewhat devoted; otherwise there is no chance of one's being purified. It is clear from this verse that even those who take advantage of karma-kāṇḍa and jñāna-kāṇḍa, but are not at least slightly devoted cannot be purified simply by following these other paths. The word prāyaścittāni is plural in number to indicate both karma-kāṇḍa and jñāna-kāṇḍa. Narottama dāsa Ṭhākura therefore says, karma-kāṇḍa, jñāna-kāṇḍa, kevala viṣera bhāṇḍa. Thus Narottama dāsa Ṭhākura compares the paths of karma-kāṇḍa and jñāna-kāṇḍa to pots of poison. Liquor and poison are in the same category. According to this verse from Śrīmad-Bhāgavatam, a person who has heard a good deal about the path of devotional service, but who is not attached to it, who is not Kṛṣṇa conscious, is like a pot of liquor. Such a person cannot be purified without at least a slight touch of devotional service.