Me estoy lavando las manos porque las tengo sucias.

English Translation

I’m washing my hands because they’re dirty.

should be tienen because the hands are dirty, not the person

The word-for-word translation of “… porque las tengo sucias” is “… because I have them dirty” which an English speaker would understand as “… because they are dirty”. That said, I would lean towards suggesting that the original Spanish doesn’t need changing, but if one were to “… porque están sucias” would be my choice. Maybe “… porque tienen suciedad” would sound as natural to a Spanish speaker, I’m not sure.

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I’m no native speaker either, but I doubt it.