Learn French: Les vieilles croyances se perdent aujourd'hui.

This is the pronominal passive. In French, when an inanimate thing (like a belief) undergoes an action without a specific person doing it, we often use the reflexive pronoun se instead of the traditional passive voice (être + past participle). Saying they "lose themselves" (se perdent) sounds much more natural in French than saying they "are lost" (sont perdues).

Does se perdent have to agree with croyances?

Yes. Since the subject les vieilles croyances is plural, the verb must be conjugated in the "they" form: perdent. The reflexive pronoun se stays the same because it is used for both singular and plural third-person subjects.

Why does the adjective vieilles come before the noun here?

It follows the BAGS rule. Adjectives describing Beauty, Age, Goodness, or Size usually go before the noun in French. Since vieilles describes age, it comes before croyances.

Is the noun croyances related to the verb croire?

Exactly! Une croyance (a belief) is the noun form of the verb croire (to believe). The suffix -ance is frequently used in French to turn verbs into nouns, much like in English.