>>1362859I recently had this exact same problem.
First, your question. I don't think rotation matters because the derailleur pivots and moves around its fixation point anyway. That would be my guess.
But anyway, personally I solved this problem just by buying a 10mm x 1mm tap, and tap handle, and cleaning up the thread with it. Somehow it fucking worked. I didn't even drive the tap through the whole thread, just the start of it (that was the only part that was fucked anyway and which was preventing me from installing the derailleur). But yeah, it worked. A miracle really. Obviously it might not work if your thread is completely fucked. But you could try it. I definitely didn't want to drill out my dropout, personally.
Also remember those dropout savers can rub on your chain when you're in your lowest sprocket. You see the hexagonal lip in your photo? That sticks out on the inside of your dropout, and yeah, your chain can rub against it when you're in the smallest sprocket. Apparently sometimes you need a spacer or something to counteract this, which isn't ideal, and I think would only work on a steel frame, because only steel frames are flexible enough to allow their stays to be spread an extra millimetre or two from their normal width.
Pic related cost me £15.30 in total ($19.23 USD). You could try it. Up to you. Depends how fucked your thread is I guess. Also if you do it, lube up your tap with something before starting - apparently WD-40 is good enough so that's what I used. If you were tapping from scratch then you're meant to use cutting compound I think, and I did actually get some of that, but I just used WD-40 for this which apparently is sufficient when you're going low speed and not generating any heat.