When used with redirects in an instance I can't really replicate offline, the website first redirects to a blank page, then the actual target.
While I wasn't able to reproduce this offline, I was able to figure out why it happened.
Pretty much, many of your files have
?> // line break here
Removing the closing tag, and the line break after it fixed everything(I did this in every file I found it in). Now, I'm guessing this happened because any extra content after the closing tag is usually interpreted as content to send, sending headers before output starts, thus breaking everything.
I fixed it in my copy of course, but that's not really future-proof, so I'm reporting this.