I want to make a mythology-inspired world, and it would be really cool to have centaur and satyr outfits (and maybe nagas) but I heard about that one infamous centaur outfit that breaks games, so I wanted to know if anyone could link me to non-game-breaking outfits?

lets start with a little history:
The "infamous centaur" "game-breaking" outfit in question is the made by Rosesims2

The reason this CC was so broken is because it was enabled for babies, toddler and children when it should have only been enabled for adults. Additionally this CC was enabled for almost every clothing category so it had a habit of being accidentally applied to sims downloaded off of the exchange.
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A 100% non broken and safe centaur outfit is made by Sil Fantasy Showcased in her Chronicles of Narnia Characters and Animals post.

I have used this outfit several times without issues. The front legs are animated and Sil fantasy used the sims3 horse model/mesh so it looks wonderful in game. This outfit requires Invisible/null feet to look correct in game, there is a download for this CC on this post.
I am super OCD about bad CC and went through Sil Fantasy Centaur Outfit removing any extra clothing categories just to be safe. You can download a CC cleanup version of her centaur outfit Here if you would like. The original download is fine it just has a few extra clothing categories enabled.

It's such a shame that the sims3 centaur outfit glitch is so infamous. The possibility of game breaking CC makes similar good CC get overlooked or avoided. Your mythology-inspired world is such a fun idea I would recommend taking a look at my Mythical Fantasy CC list (It has a Satyr and Naga section) and my Sims3 Custom Content sites and Downloads Master list to help you in your CC searching.

[QUOTE=popcornstar45]lets start with a little history:

Omigod, thank you so so much!! I really appreciate it!! <3333 Just one more quick question - I’m having a really hard time getting to the actual download link for the null feet - would it be at all possible to provide a direct link to the file?

The download for the Null feet is bundled in one download with the Mr. Skeleto CC. Here is an alternate edited download for just the Null feet. I enable them for outdoor wear.