It varies with the region & family customs.
Bengali Hindus refrain from eating non-vegetarian food on Thursdays because they believe Thursday is sacred to Bhagavatî Lakshmi. Since Tuesday & Saturday are considered to be sacred to Bhagavatî Dakshinâkâlî by Shâkta Âgamas(vide definition of Kula days of the week by Prânatoshanî Tantra), Bengali Hindus are free to eat non-vegetarian food on those days. I have also met people who refrain from eating non-vegetarian food on Mondays(not on Thursdays) because Monday is sacred to their family deity, Bhagavâna Shankara.
Hindus from Hindi-speaking regions refrain from eating non-vegetarian food on Tuesdays & Saturdays because those days of the week are sacred to Hanumâna.
Besides it is common misconception that non-vegetarian food is tâmasika.
यातयामं गतरसं पूतिपर्युषितं च यत् । उच्छिष्टमपि चामेध्यं भोजनं तामसप्रियम् ।।[Bhagavadgîtâ:17:10]
Translation: Tâmasika people like the food which is stale, tasteless, putrid & rotten, refuse & impure.
Âdi Shankara's commentary on this verse:
Stale: Half cooked;
Yâtayâma(lit. cooked 3 hours ago), meaning 'powerless' is thus explained, to avoid tautology, for the next word 'gatarasa'(tasteless) means the same i.e 'powerless'; Rotten: Cooked food over which one night has passed; Refuse: Left after a meal; Impure: Unfit for offering
Out of all kinds of animals; only goat, lamb & buffalo meat can be offered at rituals in present conditions. So duly sanctified meat can't be considered Tâmasika.