This is with the Fedora 33 package of terminator: terminator-1.92-5.fc33.noarch

I just tried to copy and paste a bit of text starting in column one from the right terminal of a vertically split terminal, but this is impossible, instead of being able to select the first char I would always get the "resize" cursor for dragging the split between the 2 terminals left/right.

I worked around this be starting the selection at the end of the bit of text which I wanted, still it would be nice if this could be made a bit easier somehow.