It's worth pointing out that vim is not "another program" as far as Neovim is concerned. It's an earlier version of the same program. Neovim is a fork of vim, not a totally different editor that happens to share part of a name.
If I fork chromium, I do not get to claim that I am a chromium maintainer.
Vim and Neovim are two seperate programs.
If it's going to nuke vim's undo files, it can't hide behind "another program".
If that's not your point, then I have no idea what you're trying to say.
From what I can gather, you can use the same vimrc file to control both vim and neovim.