Mrs. Bogart is your typical old lady next door… and not the good kind who hands out cookies and lemonade. No, Mrs. Bogart is the nosy and judgmental kind, always poking her face in people's business and telling them they don't go to church enough.
The first time this lady ever meets Carol, she remarks on how she hasn't seen Carol at church yet, and she concludes by saying, "I hope you and your husband won't have any of the trouble, with sickness and quarreling and wasting money and all that so many of these young couples do have and—But I must be running along now, dearie" (6.1.19). Yeah, let's be real: Mrs. Bogart is super passive-aggressive. Unfortunately, she's also Carol's neighbor, so Carol is too afraid to be outright rude to her.
Eventually, Carol realizes that she's going to explode if she has to take much more of Mrs. Bogart. She thinks to herself: "If that woman is on the side of the angels, then I have no choice; I must be on the side of the devil. But—isn't she like me? She too wants to 'reform the town'! She too criticizes everybody! She too thinks the men are vulgar and limited! Am I like her? This is ghastly!" (15.7.21).
The second part of that quote shows us Carol's fear that deep down, she is actually a lot like Mrs. Bogart, always trying to change the world around her to suit her own moral outlook. Of course, this realization just makes Carol all the more conscious about trying not to be like Mrs. Bogart. Does she succeed? It may depend on how you look at it.
Like many people in Gopher Prairie, Mrs. Bogart is never going to change. In fact, her entire role in this book is to show Carol just how impossible it is to change the minds of people in Gopher Prairie. Mrs. Bogart has a clear moral view of the world based on her Baptist faith, and she won't shift it for anything.
By the end of the book, Mrs. Bogart becomes infuriated with Carol's unwillingness to fall into line with Gopher Prairie, and she sure lets Carol know it: "[Let] me tell you right now, Carol Kennicott, that you ain't always as respectful to—you ain't as reverent—you don't stick by the good old ways like they was laid down for us by God in the Bible" (32.1.16). Carol won't back down, so it looks like the two of them are destined to go on disliking and disapproving of each other forever.