This is only a temporary workaround solution.
I recently had a problem with activating a very large feature in a project. I was being greeted with a 403 Response – Forbidden when trying to activate a site collection feature. I noticed that this only occurred when I had used a Forms Based Authentication (FBA) User. Seeing as how this was the only login at the time the quick thing that you can do is activate through Powershell.
Enable-SPFeature -identity “271351ab-fd87-47c0-b6cd-1c93ece7c933” -URL http://www.yoursite.com/
You will wan’t to replace the GUID with the guid of the feature you are trying to activate. This workaround was acceptable in my case however if you need to go further or have it working with FBA I would suggest looking into running code with elevated privileges as a starting point.