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If you ever have to drive very far with that spare on, it can cause damage to your differential in the rear. There is a 1" size difference between a 265/75 and 285/75, which is pretty significant for a differential to absorb. I think your stock jack should be fine....or a big bottle jack.
On the rear axle of a front wheel drive or front axle of a rear wheel drive the tire size is more or less insignificant. That's not technically true, but it works for the donut tires. Start adding heavier drivelines with limited slip and stuff like that and it makes it harder for the driveline to compensate for the different axle speeds.
Those little tires you are talking about clearly state they are for emergency use only. They have very low speed limitations on them, and most owners manuals tell you to only drive to the tire shop with it on there. Most people ignore or don't even bother to read those warnings, though. I have answered calls to people stranded on the side of the road too many times over the last two decades who have those little donut tires on their cars and they failed. Almost all of those people had been driving around for DAYS on the donut and at highway speeds to boot. If you put one of them on the front of a front wheel drive car and drive it for days, you are doing damage to your transmission and possibly the CV joints as they try to match each other, but can't. You have two tires that are traveling different distances with each revolution which = not good.