Saraswati Puja is soon coming and like any other year, my parents have told me to not study on the auspicious day. In fact, in most Bengali households, studying is forbidden on Saraswati Puja. However, at the same time, I have seen some non-Bengali families believing that it is necessary to study on Saraswati Puja. Are these just mere superstitions having a geographical/cultural divide? Or do any of these beliefs have any scriptural justification?
You should be following the customs that are traditionally followed in your own region since ages and you're not required to follow those of others, certainly not by discarding your own family\regional traditions.
So, you should be following what your parents ask you to do in this regard instead of searching how the same things are done by people living in Uttar Pradesh.
From this Chapter of the Devi Bhagavata Purana:
Right conduct is of two kinds :– (1) as dictated by the S’âstras, (2) as dictated by the popular custom (Laukika). Both these methods should be observed by him who wants welfare for his Self. He is not to forsake one of them. O Muni! The village Dharma, the Dharma of one’s own caste, the Dharma of one’s own family and the Dharma of one’s own country all should be observed by men. Never, never he is to do anything otherwise