Can't click anything on Apple's webshop

I have for some time experienced this extremely odd fault when browsing Apple's webshop. I cannot click anything. No hyperlinks, buttons, images or text can be clicked or highlighted. Everything is visible and looks normal, but I cannot click it. It's as if there's an invisible overlay in the html that covers the entire page - even the top menu.

The problem is not there when on the regular Apple.com browsing through iPhone, iMac or whatever. But as soon as I click buy or go to the webshop looking for a product I get this problem (e.g. on http://www.apple.com/dk/shop/product/MLA22LB/A/magic-keyboard-–-engelsk-usa?fnod e=9d). I've tried opening the website on Firefox and Chrome and it works fine – just not on Safari. Ironically, I have only experienced this on Apple's webshop and not on any other website.

Anyone got any idea what's wrong? It's really annoying as I use Safari by default on my iMac and don't like to switch between browsers every time I'm browsing through Apple's webshop.

Extra info

When using the 'Inspect element' tool wherever on the site referred to above, it just highlights this <overlay> container:

<overlay data-uid="dude-overlay" class="as-overlay as-overlay-popup deliverydatesOverlayContainer" data-aria-labelledby="dudeOverlayHeading" aria-hidden="true" tabindex="-1">

<materializer data-uid="dude-overlay-mat" data-shown="materializerShown" data-show-done="dataShowDone" data-hide-done="dataHideDone" class="ase-overlay-materializer ase-materializer ase-materializer-hide ase-materializer-gone" aria-hidden="true">

<computed-height data-type="document" data-recompute="recomputeScreen" class="ase-overlay-screen" data-property="min-height" style="min-height: 3717px;"></computed-height>

<div class="ase-overlay ase-overlay-popup" aria-labelledby="dudeOverlayHeading" role="dialog" tabindex="-1">

<div class="as-overlay-content as-overlay-contentnopadding">

</div>

<button class="as-overlay-close ase-overlay-close" data-ase-overlay="dude-overlay" data-ase-click="hide">

<i class="icon icon-standalone icon-closealt"></i>

<span class="a11y">Close</span>

</button>

</div>

</materializer>

</overlay>