Can I drop the second "having" in this sentence?
Yes, of course you can drop the second "having":
So, having looked through your posts and read all the materials that you referred me to, I came to the conclusion...
is perfectly fine and, in fact, better than repeating the word. The first instance of "having" can do double duty for both phrases, and it's even what the ear expects.
To me, repeating the word 'having' would be used to emphasize the fact that all the materials were read when the only thing expected by the listener was looking through the posts.