Most workshop manuals cover the refurbishment and they usually include a caution note not to split the Caliper halves.
AP issue similar advice, however, they do also say that if you do wish to split them, then replace the Bridge Seal and the Bolts. The reason they initially don't recommend splitting them is because the other parts (seal and bolts) aren't included in their standard overhaul kits
I'll add though, that while this here ^ is the official advice and really, what one should follow, I have on occasion split them and reused the bridge seals and bolts.
Personally, I do prefer to always split them to overhaul them. They are easier to strip apart, you can really clean them up - there's a few nooks and cranies that the dead sea, cows and sheep will reside in and you'll see this if you do split them. I also find it's much easier to get the wiper retainers in too.