The general case is that names in parentheses are maiden names.

However, it looks like the Barrington Congregational Church reverses maiden and married names. I have a couple sets of the membership list from that church and found the first attached image on the first page of that section.

I interpret the second sentence to say that the members are listed by the surname used when they joined the church. If a woman married later that name is included in parentheses. That would be the reverse of how we usually see, and key, them.

The second attached image is an example.

Do we just follow our usual keying guideline and hope those people will be found in a search or do we reverse our usual guideline for this church? (Or am I reading the introduction incorrectly?)

Thanks, Tom

It looks to me as though you are interpreting the introduction correctly and I think she should be keyed as Sarah W Arnold with spouse surname = Beane. (FamilySearch has a marriage at Barrington 14 Nov 1861 between Sarah W Arnold and Benson Bean to confirm this is what they mean).

That "b" abbreviation looks likely to cause confusion! Hopefully if they go through as baptisms instead of "other" it isn't likely to be a major problem for researchers, though.