So, I have just learned that you can supposedly acquire a quest from the people outside the herablist's shop to shut down his business. However, I do not receive the option to speak with any of the protestors outside the shop; Indeed, I cannot even select any of them. Are there specific times when I am supposed to approach the protestors for this?

You should be able to approach the woman leading the protestors at any time during the chapter, but try acquiring the recipe for the guy on the lower deck outside, first.

Yes, that's the problem. I can't talk to the woman at the front of the group and indeed cannot even select her (her name does not pop up). I have already completed the recipe quest.

Aye, then sadly, it's a bug. Try loading a save earlier in the chapter, if it's that important, and see whether you can speak to her then.

Otherwise, might as well forget it. Small xp and money reward. The equivalent of killing a few nekkers.