There is nothing in either the Pact rules or the find familiar spell that links the familiar to the alignment of the caster. I would allow even a LG warlock to take on a CE quasit, either in a vain attempt to prove that good can triumph over nature, or with the understanding that bending a CE demon to the cause of good has some great benefit.
If you look at the Quasit Familiar option in the MM it suggests that while it will obey the warlock like a true familiar it will goad the warlock to greater acts of chaos and evil.
Lastly, the Pact does not actually technically require a quasit familiar be CE. The Find Familiar spell does not summon an actual living creature but a spirit that takes an animal form with the beast type replace by a choice of fiend, fey, or celestial (or in the case of Pact of the Chain, an imp, quasit, etc.). I would allow a player to take bind a familiar spirit with the same alignment as them in any form. I.e., a LG celestial quasit would be available.