OK. It is a plugin conflict. 2 plugins in combination with Advanced AJAX Product Filters are problematic:
1) Advanced Access Manager and
2) All In One WP Security
I do not what exactly was the problem, but I disabled those two and it worked after. Fun part is after I’ve reenabled them, filters continued to work, so you understand why I am so lost right now, don’t you. ??
What I am trying to say, maybe few tests should be run by developers with all those plugins working together, because, they are pretty good and a lot of people is using them…
I will continue to monitor and test all this and I will update this theme if I notice something interesting which may help.