According to this fatwa , you can't touch the quran (mus'haf) if you have major or minor impurities. However, some scholars think that you can touch the quran with minor impurities, but not with major impurities:
when the quran eventually appeared in the form of the mus'haf, what were non-muslims supposed to do if they wanted to read the quran? For example, arab christians that were only able to speak arabic. In modern day, people have the internet and they can read the quran online, how would they have read the quran back in the day? As stated in the two links above, muslims sin for touching the mus'haf if we were not free from major and/or minor impurities based on the majority of islamic scholars. What about non-muslims?
How would non-muslims in the past have read the quran if they couldn't touch it as they wouldn't be appropriately cleansed from major and/or minor impurities? Would they have sinned for touching it?