[jpalomaki]

Maybe instead of blocking disposable emails, give user a gentle notification and explain why you would not like him to use such email address.

[joshmanders]

While the service mentions blocking them, this API can be used just for that. All it does is take an email and tell you if it's a temp email. What you do with that info after is up to you.

[clusterman]

+1. The WordPress plugin gives a nice warning message with a promise that the website owner won't spam or sell the email address. After all, it's all up to the website owner.