It wasn't theology at all. It's just that he was equipped with a less rigorous analogue of the Raychaudhuri equation and an intuition about the focusing theorems one could extract from it. In short: a universe with reasonable distributions of matter in it (galaxies) would collapse to a point eventually. Since the Earth was billions of years old (with improved estimates growing in age), the universe must be older still, yet it had not collapsed. Either there was a lot less matter in the universe than there appeared (and again, better observations kept finding more "nebulae" and then galaxies) or something acted against the tendency to collapse. A simple scalar multiplier on the metric tensor was a straightforward and simple way to proxy for the latter. "Static" in this context simply meant "non-collapsing over billions of years", with the value depending on the averaged matter-density.

Later he and de Sitter discovered that the multiplier could be set to zero (and consequently omitted from the field equations) while allowing an arbitrarily long -- eternal, even -- expansion of a hot big bang universe, even for arbitrarily large average matter-densities.

It wasn't until decades after his death that better observations demanded the return of the small positive cosmological constant. This time it wasn't to prevent total collapse, but rather to account for the gravitational drag of early galaxy clusters on each other not slowing the Einstein-de Sitter expansion (and even later speeding the expansion up).

The cosmological constant term was always a free parameter. It's just that there was no point in writing it down if it was measured as zero.

Think of the accolades if he'd correctly predicted expansion

To this day we would still be talking about him.

The problem is that, given relativity, he could have equally predicted collapse. There was really no reason to think it would go either way. If he'd said "the universe therefore must be expanding" he'd have been unjustified.