Very closely relates to MC-9551, but slightly different: when a minecart goes off rails or the rail underneath it is broken, the minecart texture rotates instantly to a single direction, regardless of what direction it was facing previously. This only seems to affect the block texture inside of it, i.e. minecarts themselves are not affected. Note that the minecarts themselves do not seem to rotate, just the textures.
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Does MC-226367 describe your issue?

It does, actually.