I believe in every country with non-Latin alphabet users have two keyboard layouts: local (e.g. Russian) and English/Latin. All major OSes (desktop, tablet or mobile) have install-time defaults like this, and I never ever saw any divergence from this rule, except for removing native layout if it's deemed unnecessary and going English-only, or configuring system to use some third language (e.g. a foreigner setting up a device purchased abroad, changing the defaults). I mean, I never saw anyone in their sane mind removing English layout and keeping only the local.
It is virtually impossible to use computers without having to type in some Latin characters on some occasions, like typing URLs or email addresses. Therefore, I think you may reasonable safely assume capability to enter basic Latin.
However, you should also consider that user may forget to switch the keyboard layout (happens all the time), so if you want to do some password transformations like case-insensitive password matching (due to Caps Lock), and you have significant foreign user base, you may also want to consider common keyboard layouts issues (e.g. "hunter2" <-> "ргтеук2" for QWERTY <-> Russian).
Facebook does this. This is only a single bit compromise, and if there are a lot of users affected, benefits may overweigh the slight security downgrade.
@ademarre's RFC link looks like a good place to look for guidance.