July 4th is on a Sunday, so Monday, July 5* will be observed by the USPS.  If your regular day off is Monday, then Saturday becomes your holiday.

The information below comes from the USPS ELM – Employee and Labor Relations Manual.  Click here

For Regular Carriers

518.2 Holidays on Nonscheduled Workdays

518.21 Saturday

When a holiday falls on a Saturday, the preceding Friday is observed as the holiday.

518.22 Sunday

When a holiday falls on Sunday, the following Monday is observed as the holiday.

518.23 Nonscheduled Workday

When an employee’s nonscheduled workday falls on a day observed as a holiday, the employee’s scheduled workday preceding the holiday is designated as that employee’s holiday.

518.3 Holidays on Scheduled Workdays

Holidays falling on an employee’s scheduled workday are observed on those days.

518.4 Eligibility for Holiday Pay

To receive holiday leave pay, these employees must be in a pay status either the last scheduled hour before or the first scheduled hour after the holiday or designated holiday. However, for an employee on extended LWOP, paid leave for the last scheduled hour before or the first scheduled hour after the holiday or designated holiday is not approved for the purpose of qualifying the employee for holiday pay

518.5 Provisions for Rural Carriers

(Regular) Rural carriers are not required to report to post offices for any purpose on legal holidays. When a holiday falls on Sunday, the following Monday is observed. Rural carriers are not permitted to substitute any other day.

Side note:

With the original signing of the COVID MOUs the NRLCA agreed that regular rural carriers could volunteer to perform duties on routes other than their own and on Sunday.

Effective midnight, June 4, 2021, this MOU is no longer in effect and all relevant contractual and handbook/manual provisions are now in effect. In accordance with Article 30.1.P, “A regular rural carrier shall not be required to serve all or part of any rural route other than his or her assigned route…” A regular rural carrier may no longer volunteer for these duties.

For RCAs and ARCs

Art. 30.2.P (in part)-An office-wide list will be established for substitutes, rural carrier associates, and rural carrier relief employees who desire to work on Sunday.  When there is a need to work leave replacements on Sunday, the Employer may require a part-time flexible rural carrier work prior to selecting qualified employees from the list.  The Employer will make every reasonable effort to avoid requiring substitutes, RCAs, and RCRs not on the list to work.

The Holiday/Sunday work list follows guidelines of an MOU between the USPS and the NRLCA.  See that MOU at this link