If you're using XenForo 1.5 you could either use the Alert Users or Message Users features. Alert Users sends an alert to all users matching the selected criteria. Message Users starts conversations with all users matching the selected criteria. Note that messaging users usually sends an email to all users, too, as is standard when starting a conversation with someone.
Generally all you can do is limit the number of emails you send out. If you're sending mails to your entire user base daily, then you should look at perhaps sending them weekly or monthly instead. You should also think about whether all your users need to be emailed, or whether it can be reduced to members who were active recently, or certain user groups or other constraints.
It's complicated to set up, but if you're continually sending mails out to users which result in the email bouncing (because their mailbox is full, or inactive, or it's the wrong email address) then that may increase the possibility of being blacklisted.