All memes do - that's why their name is based on genes. What's interesting is discovering clusters of memes that are self-reinforcing and are passed down consistently, without deviating too much from the original (while still allowing changes), over a long period of time. Arguably, religions built around such clusters have an easier time getting adherents and can get resurrected tens or hundreds of years after being nominally defeated or purged. So I don't think the "actual beliefs (mostly) don't objectively matter" characterization is warranted. I think they do matter a lot from the evolutionary standpoint; not so much for any of the current adherents, but for their grandchildren and later descendants.

To what extent the memetic content carries the institution versus how much an established institution contributes to propagating the content is unclear to me. There's definitely a relationship there, a complex interplay between vested interests, provided services, and people's needs and expectations. As you said, religion is much more than just a set of "nonsense" people get talked into. This makes it hard to discern the real utility of a particular nonsense for ensuring the religion survival.