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;

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;

3.Registration Statement (Form S-8 No. 333-263744) pertaining to Red River Bank 401(k) Profit Sharing Plan; and

4.Registration Statement (Form S-3 No. 333-266784) pertaining to securities that may be sold from time to time by Red River Bancshares, Inc.;

of our report dated March 16, 2023, relating to the consolidated financial statements of Red River Bancshares, Inc. and its subsidiaries for the years ended December 31, 2022 and 2021, appearing in this Annual Report on Form 10-K for the year ended December 31, 2022.

/s/ Postlethwaite & Netterville

Baton Rouge, Louisiana

March 16, 2023