Zend certified PHP/Magento developer

XHR Request recognized as a redirect

Our store is experiencing issues with adding products to the cart.
We use the QuickCartPro extension, and this always worked, but we migrated to a different server, and it broke down.

We can’t add products to our cart anymore. When we do, we see the correct URL, but the type of the request is “XHR / Redirect”, when it is supposed to only be an XHR request.
After we filter, using layered navigation, the cart works. This continues to work, even when removing the layered navigation. The redirect request returns a 302, but that leads to a non-existing page, an

So, it seems that our store has a problem recognizing URL’s.
This happened after we migrated and installed Varnish Caching, which shouldn’t be an issue in my opinion. It has always worked before that.

If anyone has a way to maybe force Magento to see it as an XHR request? Or any other experience/solutions that might help us out?