It looks like someone, at some point (back in the days of SVN) was trying to implement the 'standard' isothermal collapse problem (e.g. Burkert & Bodenheimer 1993). However, they did it incorrectly - the 'standard' problem is a m=2 perturbation on a uniform background density profile - and in such a way as to make some possibly useful choices - a cored sphere and a Bonnor Ebert sphere - incorrect in a non-obvious way.
I guess these choices aren't used terribly often since it's been in the codebase for so long, but having just found a use case for a collapse test with a cored sphere, I vote that the hard-coded m=2 perturbation should be removed.
I think I was a bit hasty yesterday when I said that NFWCoolCoreCluster might be affected. NFWCoolCoreCluster defines ClusterSphereType, which is a totally different parameter compared to CollapseTestSphereType. Looking at the run/ directory, all the extant tests use ClusterSphereType = 1 or 2, so this PR shouldn't change any answers.