Exhibit 23.1

CONSENT OF INDEPENDENT REGISTERED PUBLIC ACCOUNTING FIRM

We consent to the incorporation by reference in the following Registration Statements:

1.Registration Statement (Form S-8 No. 333-232404) pertaining to the Red River Bancshares, Inc. 2018 Equity Incentive Plan and the Red River Bancshares, Inc. 2008 Equity Incentive Plan; and

2.Registration Statement (Form S-8 No. 333-236300) pertaining to Red River Bancshares, Inc. and Red River Bank Amended and Restated Director Compensation Program;

of our report dated March 18, 2022, relating to the consolidated financial statements of Red River Bancshares, Inc. and its subsidiaries for the years ended December 31, 2021 and 2020, appearing in this Annual Report on Form 10-K for the year ended December 31, 2021.

/s/ Postlethwaite & Netterville

Baton Rouge, Louisiana

March 18, 2022