Is there a mechanism that allows me to “unsubscribe” from comment notifications on my answers? Ideally something that operates on a per-answer basis. Alternatively, can I mute certain people so their rants do not result in a notification?
There isn't a way to turn off notifications for comments on your posts. I've personally found a long series of comment notifications unwelcome on a few occasions. But I guess I am glad they can't be disabled since comments sometimes convey very important information.
The general attitude towards comments on SE is that they exist to help people work towards improving posts, though they do sometimes have some other kind of value. Once the improvement to the post has been effected, comments ought to be no longer needed. They are considered to be of transient value at best (though a substantial minority at least are worth keeping around).
Because of this philosophy of comments, it is felt that they may be removed casually. If a person has something of lasting importance to share, they had better put it into a post.
So, you should not hesitate to flag comments that are not of value. Comment flags are rarely declined. One of the things I try to do every time I visit any question or answer on Ask Ubuntu is scroll through the page looking for comments that can be cleaned up.
NB: This doesn't apply to meta, which, unlike the main site, exists in part to allow and preserve discussion. It's rarely desirable to remove comments on meta. However, if someone is trolling you with comments on meta do go ahead and flag.