You made some good points. I will agree with you that CSR does have an important part to play in the company's activities, such as in responsible use of its surroundings. You said it well when you say that corporations are somebody's neighbor. If a corporation's activities are going to negatively affect (or potentially affect) the people nearby (e.g. through environmental pollution, noise pollution, increased traffic, etc.), it has an obligation to those people and not weasel out of its responsibilities. A corporation also duties to its employees. So while profit is a significant goal of a corporation, it is not the exclusive goal.
With that said, I disagree with some of the other points. You seem to be saying that "image is everything" and giving money to causes helps repair that. This means that whoever dominates the cultural narrative gets to regulate the behavior of corporations; since leftists control our major cultural institutions and media, their voices are heard and their plans are implemented.
Think about it - when a company supports gay marriage or Black Lives Matter, the national conversation will speak of that company with praise. Meanwhile, a company like Chik-Fil-A, whose CEO personally opposes gay marriage, is treated like a villain. Hobby Lobby is another example. The "brand image" of these companies is very negative in some circles because leftists get to frame certain cultural perceptions and conservatives do not.
I can understand the desire of corporations to avoid bad press because it may hurt profits. However, at some point corporations have to have some backbone and tell the media to jump in a lake and stick to its principles regardless of brand image. The left does not get to dictate right and wrong, but they will continue to do so as long as we let them.