Except this bill doesn't force religious institutions to perform any such service. This is about legally recognizing these marriages.

​

From the text of the bill:

SEC. 6. NO IMPACT ON RELIGIOUS LIBERTY AND CONSCIENCE.

...

(b) Goods Or Services.—Consistent with the First Amendment to the Constitution, nonprofit religious organizations, including churches, mosques, synagogues, temples, nondenominational ministries, interdenominational and ecumenical organizations, mission organizations, faith-based social agencies, religious educational institutions, and nonprofit entities whose principal purpose is the study, practice, or advancement of religion, and any employee of such an organization, shall not be required to provide services, accommodations, advantages, facilities, goods, or privileges for the solemnization or celebration of a marriage. Any refusal under this subsection to provide such services, accommodations, advantages, facilities, goods, or privileges shall not create any civil claim or cause of action.

https://www.congress.gov/bill/117th-congress/house-bill/8404/text