Animal shelters are often non-profits run by a hired manager and a number of paid and/or volunteer employees. All of this is overseen by a board of directors.
If I were a betting man, I'd wager the person who sent you this email was some individual with a personal burr under his or her saddle, not someone speaking on behalf of and with the blessings of the organization.
I'd be careful how far I went with this line of thought. After all, if it's really the animals you're concerned about instead of the ad revenue, then removing the ads should be an easy decision. Pick your priority, stick with it and proceed from there.
Not long ago I purchased a box of old photographs at an estate auction. One of the photos showed the grand opening (from 100 years ago) of a retail store in a particular nearby city. I advertised that photograph for sale on craigslist. Someone emailed me and told me historic items like that belonged in the local museum and I was subject to a fine and imprisonment if I kept it and didn't donate it.
I got a good laugh out of it. I suggest just ignoring such small-minded and anal people.