The obligation is that you give applicants (and employees) the opportunity to voluntarily self-disclose race/ethnicity, sex, disability status, and veteran status. They are not required to fill out the information since it is voluntary. Here is language commonly used along with the self-identification form. "When you apply for a U.S.-based job with COMPANY, the federal government requires us to ask you for information such as gender, ethnicity and race, disability, and veteran status. Sharing this information is completely voluntary. Declining to provide this information does not affect your application for employment in any way."
You can use this OFCCP audit checklist to ensure you're doing what is required to maintain OFCCP's regulations including VEVRAA, Section 503, and EO 11246. Or request a demo to streamline your compliance and recruiting efforts.