The width with the mirrors is probably not the big issue. It sounds as if it will be the size of the gap you have left to get in and out of when the door is opened as far as you have room for.
Other things being equal, the longer the door the worse it will be.
I suspect the MINI has thicker doors so you might be OK. The MX5 also has frameless doors so you can have the window down and / or the roof down if you need to.
I used to keep my ND soft top in a garage IIRC 2.2 metres wide internally . I would park it with the left mirror an inch or two from the wall on that side, and open the driver’s door on to a piece of carpet I had fastened to the wall on the other side. The carpet was really helpful, I’m sure I would eventually have knocked some paint off the door without it.