Dungeons and Dragons Character Creation Preferences

I do all of the above depending on the setting and campaign. We did a game of monsters once with any race open as an option so long as they could be "created" using a set of monstrous race rules, based on points. Other times I have done human only, limited classes, or opened it to Unearthed Arcana or homebrew. The freedom or restrictions should depends a lot on the type of game, in my opinion.

I played a campaign where limit on race or class were based in settings and explained by DM on session 0. it felt so natural. I don't like games where PCs are from 5 different sorcebooks like warfoged+owlin + Thri-kreen + ....
On the other hand it feels strange when limits are defined mechanically with no good thematical reason.

I like no extra limits, and that is because I prefer 1ed, where the limits are already built in (no human multi-class, minimum and maximum stats, etc.)

I feel that constraints helps funnel the creative juice's. My initial idea needs to be distilled into something that is fun to play for the duration. Sometimes that is achieved through restrictions.
But then in AD&D then there is a million splatbooks

run it wide open, haven't come across anything that breaks the game yet.

2ed had the gazillion splatbooks. 1ed had just a few. OA? Wilderness, Dungeoneers, IIRC.

Splatbooks??

Complete book of Dwarves
Complete book of Elves
Complete book of Gnomes and Halflings
Complete Fighter's Handbook
Complete Ranger's Handbook
Complete Paladin's Handbook
Complete Wizard's Handbook
Complete Priest's Handbook
Complete Druid's Handbook
Complete Rogue's Handbook
Complete Bard's Handbook
Complete Ninja's Handbook
Complete Psionic's Handbook
Complete book of Necromancers
The list goes on and on for AD&D or D&D 2nd edition

Good reasons help define a world and setting so limits in those cases are great. Where the setting is generic or broad enough to encompass everything (like Forgotten Realms), limits seem . . . limiting.

QFT

I'll usually add limits to myself based on what I know about a setting if not already given limits because I find being limited in options both helps me make choices but also to some extent can force you to build more of a character than my character is elf wizard.

no limits helps keep me educated about the game. a player used grievous wounds (drakkenhiem) on poor strahd, striped him of all immunities and made him vulnerable to all dmg for a turn, ha. guile of the cloud giant, hit player with attack roll they have resist vs the dmg and can teleport 30' away (glory of the giants). artificers and all their items...

Honestly, it depends on the campaign setting. In the Forgotten Realms, Drizzt has softened the feelings towards dark elves, whereas in Greyhawk, drow are pretty much universally regarded as evil, and they simply do not exist at all in my homebrew setting. Can you play a warforged not in Eberron? Sure, if the GM allows it, but they will be out of place, regarded as a curiosity at best, and some kind of golem at worst. If it's just that I, personally, hate bards (as an example), that's not a good reason to exclude them. But, if I'm running a setting where all bards are arrested on sight, then the players probably should be encouraged not to or restricted from playing one (or at least made aware of the risks of such).

I've actually found that, with one notable exception, campaigns where I run something that should be evil (goblin, lizardman, yuan-ti, etc.) I have to actually work hard to get people to treat me badly. Everyone seems to ignore it and just move forward. Heck, orcs and tieflings are in the base species in the PHB.

And, where it fit the setting (running a Nord Stormcloak in a Skyrim campaign) and I've tried to be a bit of a xenophobe (just verbal, not starting fights or acting out), it made everyone else so uncomfortable that I quickly removed it from my playstyle.

So, yes, I think the GM has to be the tone setter in this regard. And I say this as someone who loves running the fish out of water, despised and looked down on types.