I don’t think that the appearance o the word “either” changes the general rule – if you’re not specifically told “but not both,” then “or” is inclusive. For instance, “To be accepted to college, one must have either a high school diploma or a G.E.D. Certificate” would not be logically incorrct and would not imply exclusivity. I haven’t checked, but with one exception, I strongly doubt there are any situations where it’s supposed to be the exclusive “or” and they don’t say “but not both.”
The exception would be situations where the inclusive ‘or’ would be impossible. For instance, in a 1-to-1 sequencing game where it says something like, “X is in position 3 or position 5.”
When I say “but not both,” I mean to include any such similar limiting language.