Digital Light & Color

When a Clone side branch is added, it will ask for Profile conversion confirmation if there is a profile mismatch.
Considering that it is a clone of an existing part of the tree, I would say that is should just copy the original top input image (whether it was confirmed or not), otherwise the starting (top) image of the cloned section of the tree would not be the real clone and the following images might look differently without a visible cause. To find out or to make sure why, you have to go to Properties of both top images.

I think that if you want to compare results using different profiles, a better way is to insert the conversion step into the clone branch. You can see that Conversion step and you can even play with different profiles.
Also, if each of the top images had a different profile and you still wanted to insert Profile conversion as a step in one branch, then it would be impossible to make anything out of this double conversion.

If you want to compare two branches based on the same file, try cloning a side branch from the first transformation below the File Open and not from the File Open itself. Creating a side branch on the File Open is more useful when you want to compare the same processing on different files. The reason you are getting asked a second time for the profile conversion is that the same file is being read in a second time. Asking for a profile is important if you are executing from a script.