I can't reproduce this, for me when I press F2 it goes immediately to #2 above, and then cycles as you describe. Since the fix it never selects just "one" as far as I can tell.
Hi Jon.
Okay, here's how to reproduce it.
In Prefs / Inline Rename / pull-down, I have "Cursor before extension".
(I "lied" about step 1. It is not that it selects "one", but that the cursor is after "one" instead of after "two".)
I tried "Select filename stem", which I assume you must be using, and verified that it is working perfectly.
But in the past weeks I have been enjoying "Cursor before extension", and that's where the small residual bug seems to live.
Sorry for not describing the problem accurately, by the way, hope I didn't waste too much of your time.
(Interestingly, "Cursor at end" seems to do what I'm looking for with "Cursor before extension", perhaps because I'm in that "hide extension" mode you mentioned before.)
Wishing you a relaxing Sunday.
Thank you for the fix in 10.2.0.3 beta. Works perfectly on my end. 
+1 Great job guys!
Not sure if it's better to open a new question, or add to the existing one, but I seem to be having the same trouble that Playful was having.
I have a "Filename" column and an extension column (because extension is shorter than filetype).
Under Display, I choose "Hide file extension in the filename column".
I've tried every possible option for Preferences / Inline rename, only:
Default Selection Mode - Select Extension will allow me to rename the file extension inline.
Personally I would like to be able to use "Select filename stem" and when I need to just tap the right cursor a few times to change the extension. For me, "Select Extension" by default is not a good option this way I'm likely to have a typo turn into changing a filetype so that I don't find it again...
For some reason I can't edit this post like I can most of my other posts... Strange...
Anyway, wanted to add that I'm on Opus v12.3
If extensions are hidden you can edit them from inline rename by pushing ctrl-e while renaming.
If you're only moving the extensions to a separate column so that you can sort by them, note that you can do that with just the normal name column and extensions shown normally, by holding shift and clicking the Name column header. The sort arrow will point left or right, instead of the normal up or down, to indicate you are now sorting by extensions.
Thanks, I wasn't aware of CTRL + E. As usual, you guys have a solution!
In my case, I've got a small screen (Surface 4) so I prefer using extensions instead of the "file type" column. If you can think of another visual realestate saving method I'm open to suggestions 