Adding a few thoughts for consideration to this old thread. For reference, my experience spans all D&D editions from first edition to current.
As previously stated, Find Familiar spell (found in the Players Handbook p240) forces the caster to choose the creature type when they gain the spirit's service. The players chooses if "it is a celestial, fey, or fiend instead of a beast." This choice entirely replaces the original creature type. Now, if one were so inclined to align a familiar, one might use the choice of creature type as guidance. (From the Monster manual the following is true.) Celestial creatures are overwhelmingly Good, Fey - Neutral, Fiends - Evil. (makes sense thematically)
Personally, my experience tells me that I like some of the ideas presented and would use what makes sense for the character running the familiar and for balanced play. For example; If a good aligned character wanted an evil familiar to have role playing moments that create interest for the player, I would consider it. Although, I have a hard time seeing for example, a Celestial Evil Imp.
I'm all for inventive play. However, my experience tells me to steer away from detrimental game mechanics. I don't allow players to abuse a mechanic to bypass a story hook or any reason for that matter. And, swapping alignments around is firmly in the realm of powerful effects such as curses, planar effects, artifacts and the like, not a first level spell that is also a spammable ritual. Magic is powerful but first level spells are not that powerful. That said, I encourage inventive play and work with players to create a live environment that all players can immerse themselves and enjoy their characters and story.
To be sure, the Players Handbook notes the ability for player characters to change alignment. This requires storytelling and potentially role-play to accomplish.
I do like the idea of the caster aligned (makes sense thematically) and the unaligned familiar also since you can essentially transmute its form when you recast Find Familiar. Keep in mind, a familiar is much more than a basic stat block. It is a part of and an extension of the caster.
D&Ders, what ever you decide, have fair fun!
D&D 5E Alignment Information Sources:
Players Handbook - p122 Alignment in the Multiverse "Alignment is an essential part of the nature of celestials and fiends. A devil does not choose to be lawful evil, and it doesn’t tend toward lawful evil, but rather it is lawful evil in its essence. If it somehow ceased to be lawful evil, it would cease to be a devil."
Monster Manual - Creatures
Dungeon Masters Guide p59-60 - Bytopia - Pervasive Goodwill: visiting the plane of Bytopia causes a shift in alignment to NG or LG.
Dungeon Masters Guide p138-139 - CURSED ITEMS
Dungeon Masters Guide p162 - The Deck of Many Things Balance "Your mind suffers a wrenching alteration causing your alignment to change. Law to Chaos, Good to Evil and vise versa"
Dungeon Master's Guide p97 - Oathbreaker paladin atonement rules. "The paladin who wishes to atone must first shed his or her evil alignment and demonstrate this alignment change through words and deeds."
Players Handbook - p122 Alignment in the Multiverse "For many thinking creatures, alignment is a moral choice. Humans, dwarves, elves, and other humanoid races can choose whether to follow the paths of good or evil, law or chaos."
Additional information added here by me from posts by Phil Boncer and from post by Liza's Mentor.