[Antoninus]

There are good studies which show that as much as 50% of the population had become Christian and that this was having an effect on the military.

You'll have to provide some sources for this claim. I have never seen anything like the empire being 50% Christian in the early 4th century in any serious scholarly work. Maybe by the end of the 4th century, but during the Great Persecution or early in Constantine's reign, no way.

That said, there were definitely Christian units in the army from at least a century before Constantine:

When rain saved the Thundering Legion ~ Legio XII ~ during the Macromannic Wars of Marcus Aurelius

[wbarmy]

“By the beginning of the 4th century, and the reign of Constantine, civil wars and foreign incursions had taken their toll. The number had grown again, likely to somewhere around 55 million,”

https://www.unrv.com/empire/roman-population.php

He estimates that because of these reasons in 350 AD there were 33.9 million Christians or 56.5% of estimated population of 60 million.

https://thehlukejourney.wordpress.com/2017/04/02/5-reasons-christianity-increased-to-56-of-world-population-by-350-ad/