What color do parents wear?

They should wear whatever they are comfortable wearing. They don't need to match your bridal party. The bridal party and parents aren't normally in a lot of photos together so it won't matter.

They can wear whatever they'd like, they don't need to match your bridal party or coordinate with your decor.

We have navy blue & mauve so we split it , we have his parents navy blue and my mom wedding mauve my dad with a mauve tie but navy blue suit

If they’re asking you for suggestions then I think it’s fine to let them know those are your colors and just let them decide

Any color that is flattering is fine. They don't have to match your colors

Our wedding colors were dusty rose, dusty blue and gray. The groomsmen wore gray and my dad had on a black and gray tux. The bridesmaids wore dusty rose and my mom had on a blush color and my MIL had on a silver/gray.

They should wear what they want. Traditionally, the mother of the bride will choose her dress and then the mother of the groom chooses hers so that they don’t have the same color or identical styles. Normally, they all try not to clash with the bridal party or each other, but that’s a matter of personal preference.