Not familiar with them at all, though I will note that they have published Brian Aldiss (a book of poetry), as well as Joe Haldeman and Jane Yolen (in a poetry anthology). That seems to give them some cred, at least.
Other than those writers -- more known for their fiction than their poetry -- I don't recognize anyone they publish (that I saw in my short stroll through their catalogs). But a reading fee for an established poetry press is not so outlandish in my experience. The trick is figuring out whether they are established and respected and, in the final tally, whether you'd feel proud to be published by them.
A vanity press is generally one looking to make money off of the authors. Best case scenario here, you pay $20 (when their submissions are open) and get a book published plus a "royalty" of 5% of the print run. So no cost to you except for the reading fee.
However, they go out of their way to point out that they do little to no marketing or distribution beyond their website and local events. A number of the poetry presses I know about and would love to be published by are very dogged in their determination to get the books out into the world, while Mayapple says that their main goal "is to help you publish a book which is physically beautiful as economically as possible and without long delays."
So, vanity? I'd say not. Is being published by them going to get you what you want out of a publisher (and a published book)? That's up to you. It wouldn't be for me.