I actually giggled when the original poster asked if they cd require an actor to have email access - no offense, really - it's just, I am of an age when you typed everything up and ran off copies for all departments before you left at night, when calls to all the actors abt schedules happened daily (before hotlines even), when the daily changing info posted on the callboard and the nightly phone calls were considered SOP. (side note - yes, investing in a portable callboard is worth the $20 and definitely worth the hassle to schlep it - even in this day and age, there are theaters and tour housing without email access or local phone access, and people without cell phones. Really.) I seem to do a lot of shows with seniors and luddites, and we still use old school methods of info for at least 1-2 people in almost every cast.
No, you can't require an actor to have email, or a cell phone, or any other mode of direct contact. You CAN require them to be responsible for themselves, for checking w you and making sure they have the correct sched for the day - and to not complain abt suffering the consequences if things change and they can't be reached for notification.