Should I sign a processor agreement that my customer sends me?

Signing is not an obligation, checking is

No, there is no legal obligation to sign a data processing agreement simply because a customer provides one. A data processing agreement is an arrangement between two parties, and like any contract: you first look at what it says before you sign. The customer who sends the agreement does not automatically determine the content — that content must meet certain requirements, and that is different from "must I accept this document".

What is relevant: if you as a processor process personal data on behalf of that customer, the GDPR requires that there be a data processing agreement with a number of mandatory components. So it is not about whether you sign, but whether the text you receive covers those components and aligns with what actually happens in practice. A draft that is formulated too broadly, regulates things that do not match the actual service provided, or is missing components, is a reason to adjust or propose your own version — not to sign without question.

What Article 28 GDPR regulates on this

Article 28 of the GDPR provides that processing by a processor must be governed by a contract or other legal instrument, and lists the subjects that must be addressed — including the subject matter and duration of processing, the nature and purpose, the type of personal data and categories of data subjects, and the obligations and rights of the controller. That article says nothing about who drafts or provides the document; it only says what must be in it. For the full text, the regulation itself is the source, and in case of doubt about a specific text, the knowledge base of the Dutch Authority for Data Protection can serve as background — although that authority does not assess individual contracts.