Square (1:1) photos are not exported as 1:1

xinux s right. Crops in Lightroom are done in fractional values. They are stored as floats and you can indeed crop in the middle of a pixel which could result in a 1-pixel difference between the horizontal and vertical dimension if you for example crop horizontally at pixel 100.25 to 1100.65 (which would give 1002 pixels) and vertically to pixels 200 to 1200.4 (rounding to 1001 pixels) even though the horizontal and vertical crop dimensions are identical. Lightroom should recognize this though and normally you shouldn't be able to make crops this way but there are cases in which it can happen such as syncing settings or applying presets..

Lightroom cannot crop on export, you have to do that first. So if the exported photo is not exactly square, then you did not crop it to an exactly square format.