What are the reasons to disallow plug signs in email addresses?

From an input-validation standpoint, they have no leg to stand on; there are a specific set of RFCs that robustly describe the format of a valid email address. Even if an email address is technically invalid according to the RFC, it may still be possible to deliver mail to it anyway. You can check if an email address is deliverable by sending mail to it with a unique link for the owner to click on. As the linked site says:

Sadly, many websites won't let you register with a plus sign in email addresses. Not because they are trying to defeat your tracking strategy but just because they are crap. They've copied a broken regular expression from a dodgy website and they are using it to validate email addresses. And losing customers as a result. Even if we assume they have completely broken code and they are using a crap validator because they literally paste the validated email address into a UNIX shell, that still doesn't give a valid reason why joe.bloggs+meetup.com.better.not.sell.this.to.spammers@example.com should be considered invalid.

There is no valid security reason to ban the use of + in email addresses. Even if spammers use it as a low-rent way of making multiple accounts, websites can easily see if someone signed up both as joe.bloggs+1@example.com and joe.bloggs+2@example.com; if Joe Bloggs is abusing their service, they can easily ban both accounts. Anyone with their own mail server can generate valid email addresses like joe.bloggs1@example.com, joe.bloggs2@example.com. They gain no additional security by prohibiting the use of +.