Custom Menu Anchor Links Not Working

First: congrats!

The links are well formed, so that is not your problem.

<a id="rsvp" rel="m_PageScroll2id"></a>

Is not the convention in HTML5 anymore. You should prefer to put the ID in your H2 element. Something like this:

<h2 class="entry-title" id="rsvp">RSVP</h2>

Using Google Chrome, when I tried that, I still got the same problem: your entire page goes blank on my client when I click on the link. Your error is not with the link structure. I strongly suspect that the theme has an error in the styles or the java script that accidentally causes all text and images to disappear.

But, at least you know that your links are fine.