jQuery works fine in Tumblr. I've tried moving this line from header to footer:
<script type="text/javascript" src="http://cdnjs.cloudflare.com/ajax/libs/gsap/latest/TweenMax.min.js"></script>
I've also tried switching themes multiple times. I've even tried using jQuery's .getScript() to bring in such CDN's from multiple different sources without any luck.
It works FINE when the HTML file I'm using these libraries with are hosted on my own computer.