There was an HN discussion in 2020 about the oldest business or commercial establishment in various countries and/or continents. Many of those are involved with, variously, food service, alcohol, teaching, construction, or banking. In part because those are activities which have been with humans (or at least civilised, that is, inhabiting-cities humans) since the beginning, and have not been supplanted by some newer activity.
The Church requires that you've decided this needs to be organized, all you need to start praying before you go hunt for food is superstition.
The Princes Alice experiments show why superstition might be valuable (and so get preserved in a culture) if you don't have much technology to provide oversight. Children were told to perform a task and that an (invisible) Princess, Alice is watching to check they don't cheat while the adults are away. Superstitious children didn't cheat because they believed in Alice watching them. The non-superstitious children cheated, after first verifying that in fact Alice does not seem to exist (e.g. passing their hand through space supposedly occupied by the invisible princess)
That interpretation only works if you desperately want the comment containing the phrase "the church" to be wrong. If you insist on this unusual interpretation, then yes, farming isn't at least five times older than the church. But if you go with the usual interpretation of "the church" as a metonym for Christianity, as was very clearly intended by the implications of the statement, it is correct.
Why not go talk to some Muslims about the Islamic church? Or some Hindus about the church of Shiva? I'm sure you'll find the discussion edifying!
