Websites which carry advertising must negotiate a licence fee with Unisys. Switch to a non-patented graphics format, burn your GIFs to call attention to the fact that you're doing so, and avoid patent minefields in the future. The actions are meant as symbolic rather than militant, and the organisers have stated that it will be a peaceful event and that participants must obey all applicable laws and regulations. The site offers dozens of conversion utilities, and popular graphics packages can write PNG files and most browsers read them as easily as GIFs. We would ask you how you were creating your GIF images, and we would expect you to answer truthfully.
Many sites generate images on the fly, for stock charts, web hit logs, and other graphics.
Any site that develops its own system to generate a GIF on the fly would have to negotiate a licence. The League's agenda extends far beyond the issue of GIFs, and lays the blame for the current situation with the US Patent Office.