I'm not saying that it doesn't exist in perhaps specialized applications but ... I have never ever seen an automotive fan belt that was a möbius strip. Older cars (and other belt driven machinery like drill presses and band saws) use v-belts and newer cars use serpentine belts. Having installed new belts in both my older and newer cars (as well as the drill press and band saw in my shop) I have seen exactly zero that could be called möbius. In fact, I don't recall seeing one at the parts store that was möbius. In fact, now that I think about it a serpentine belt comes in contact with rollers on both faces anyway and would not have to be möbius to wear more evenly.
I don't know where you're based but they were never common in the USA, and where they were common they have since been replaced by modern materials with a clear inside and outside and no twist.