Why is there no "who" in "ex-soldier turned religionist"?
Solution 1:
As Andrew Leach noted, turn can mean become. It is often used when what the subject became is notably different from what it was previously. In your example, being a soldier is thought to be violent while being a religionist is thought to be peaceful.
Other examples might include homophobe turned civil-rights activist or Windows user turned Mac fanboy. It's not limited to people: ... the dog, obedience school star turned vicious attacker ... or the once grand mansion turned haunted house ....
I suspect that the idea is that the subject was one way, then did an about-face to embrace something different, hence the notion of turning.
Edit: On the subject of who:
It seems that in this construct, ex-soldier turned religionist, the ex-soldier turned part is acting as an adjective for religionist and, together, they are all acting as a noun -- the thing that the unique individual was.
If you added a who in there, it changes the emphasis:
This unique individual was an ex-soldier who turned religionist.
Previously, this guy was simply an ex-soldier-turned-religionist but now, he was an ex-soldier who did something -- he turned religionist. In the original the emphasis is on him being a religionist (who was once an ex-soldier) while the new version defines him as an ex-soldier and adds the action of becoming a religionist.
What you use would depend on how much you want to highlight the act of changing (even if it's still a very slight emphasis) as opposed to just stating it as fact (the having turned) and moving on.
There's not much on the question of who there, but you might still want to take a look at Meaning of “singer-turned-actor-turned-writer-turned-politician”