Learn Italian: Questo fanatismo li spinge a venerare l'attore. - This fanaticism pushes them to worship the actor.

The verb spingere (to push or drive) requires the preposition a when followed by an infinitive. The fixed pattern is spingere qualcuno a fare qualcosa (to push someone to do something).

Why do we use li instead of gli for "them"?

You must use li because the verb spingere takes a direct object (the person being pushed). Li is the masculine plural direct object pronoun, whereas gli is an indirect object pronoun (to/for them).

How could I express this extreme limit using the current lesson's grammar (al punto da)?

You could rephrase the underlying idea as: Sono fanatici al punto da venerare l'attore (They are fanatic to the point of worshipping the actor). You use al punto da + the present infinitive (venerare) because the implicit consecutive clause shares the same subject (they) as the main clause.

Does venerare need a preposition before its object?

No. Just like "worship" in English, venerare is a transitive verb, meaning it connects directly to its object without a preposition. That is why it is directly followed by the noun phrase l'attore.