I do not want to display related links on my home page posts, mainly to conserve space, and since I only show excerpts on the home page. This could of course be an option, though, for those that want it.
Another possible reason, is SEO-related - having too many internal links from your home page can be a bad thing. (Maybe there can be an option to make the related links "nofollow" too?) That's in addition to the "duplicate link" problem, because many of the related post links on one's homepage are going to be the same.
How this rule be written, I don't know exactly, since I'm not a programmer, but if I look at some other plugins, I may offer some suggestions. For example, the AmazonFeed plugin has a "Display" function with home page and other options in its admin backend (see http://imm.io/gBFb ). Maybe something similar can be offered in your plugin?
I previously used the Related Posts by Tags Widget plugin, that has functionality similar to yours, except no admin settings (although it has the option to display related posts in feeds, as well as dates next to the related post links). I have stopped using it because it's outdated and I have started seeing database errors on some of my sites. But that plugin doesn't show related posts on the home page - not sure why/how, but maybe you can take a peek? ;)
Finally, I like your plugin, but have one bit of criticism, if you don't mind. There is a "Plugin Updates" section in the plugin admin settings that "phones home" to display any plugin updates. I've had a problem where this "update notice" couldn't display, apparently due to a network/website issue or because it couldn't find your server, resulting in the settings page not displaying, but just "polling" endlessly. I therefore feel this function is unnecessary and intrusive, firstly because we are not made aware of it (it's a bit like spying" on your users), nor have the option to turn it off. And, secondly, the "update" function is not needed, since WordPress already provides that when the plugin is updated in the repository. And, lastly, as I pointed out, when there is a network/connection problem it negatively affects the user's website. So, I would suggest you seriously consider removing this "feature" all-together. (It may actually be a contravention of the WordPress plugin guidelines - see #7 here, for example) In this vain, why is there a function to email you on line 172? Just saying... I trust you will see this as positive criticisms.
Thanks again for your contribution and hard work! :)