Does the Catholic belief that God dwells in the tabernacle via the Real Presence contradict Acts 17:24?

The short answer is “No, it doesn’t!” Consider that what Paul meant—and what his audience would have understood by a deity living within a shrine—is the Greek understanding of divine-temple indwelling. For the Greeks, their deities dwelt within the walls of Greek temples and nowhere else, especially because they believed their deities dwelt within the carved statues located within their temples.

Such a pagan understanding of divinity stands in stark contrast to the Christian understanding of God, who is omnipresent—existing in all places. It’s this contrast that Paul is drawing out for the Greeks in Athens.

Paul intends to target the Greeks’ view of divinity and their worship that they give to such divinities, and he says that such belief and worship are false. And he offers Christian belief and worship in their place.

With this in mind, it becomes clear that Paul is not rejecting the idea of divine-temple indwelling absolutely speaking. Rather, he’s rejecting the Greek view of divine-temple indwelling.

So, Paul’s teaching in Acts 17:24 doesn’t conflict with the belief of God dwelling in churches via Jesus’ real presence in the Eucharist.