The goal should be attracting customers that want to read your emails. If they are using disposable emails, that means you do something wrong. Maybe you should skip email requirement?
If you force the emails on them they are only likely to become annoyed at your company and reduce their interactions with you.
Do two things. Make the email address optional. Make the email content so desirable that the customers provide their real email address at their own free will. It's the best of both worlds, now you only have email addresses in your list of people who are genuinely interested in seeing your content.