How to unblock these redirect sites?

Basically these are redirect sites for websites like Newegg etc, right now I have to copy the redirect url and clean it up to get to the correct site.

Below thread sums it up great on how to block the sites but I want to allow them.

https://adblockplus.org/forum/viewtopic.php?t=531

Example links for one site can be found here

I'm not sure if I understand your question... If the redirect websites are blocked by entries in the blocking lists, you can unblock them by adding them to your whitelist.

I've added dpbolvw.net already to my whitelist,. Prior to adding to the whitelist when you click the link the page just opens and closes quickly, it's exactly the same after whitelisting.

The redirecting is probably still cached in your browser:

To rule out caching on client side, you can use the nslookup command on a client to test eg:

nslookup <DOMAIN> <DNS_SERVER_IP>