Seems that customizr is not the reason you get blank pages.
I created a sample wordpress blog where I installed both customizr and Inlinkz and they seem to get along nicely. The widget is even visible inside customizr’s edit dashboard
(see here: https://188.226.177.44/?p=1)
or
https://www.evernote.com/shard/s44/sh/5cf4beae-0641-4b9b-82eb-163505f417cf/f5d4ca8e6fa0c1ec9d217d8e1df552d0
I used both the raw code for InLinkz and the plugin for it to test it.
What you can do is disable plugins one by one, while running the customizr to see if one of them is causing the trouble. For example, a pinterest button plugin that may freak out due to the existence of lots of images.
let me know through the inlinkz support page if you need any help
Aris