To my mind, from and of have different connotations.

To free HK from bottles implies to me at least, an ongoing situation. What’s more, Hong Kong’s government is no longer dealing with plastic bottles.

Why are HK plastic bottles banned? A lot of people have outgrown their bottles waiting to be taken out. Something has to get them out of the way. What does it say about the past, not necessarily address the future situation, but only the way it is now based on past usage.

As for rid versus free, I think they’re pretty much equivalent, although free does somewhat suggest unshackling, if you will, rather than just getting rid of something. What is it like that plastic bottles are mainly problem in HK? If there is a lot of animals nearby, be rid of them.