OK, well I don't have my face and mouth in close contact with the "seat used by others", so I'm not sure how that's relevant. Unless the suggestion is that we just reuse the bedding without having it laundered. Good luck selling that one to J passengers.
The "war on plastic" is a very blunt instrument and arguably more to do with PR than reality. In many cases, use of plastic as an implement or barrier is far cheaper and environmentally sensible than alternatives, and it's used to prevent over-processing (including cleaning, which requires energy and chemicals) or waste. You have to be careful to consider the entire environmental impact of any artefact rather than greenwashing the obvious front end things.
The idea that eschewing a straw in your onboard drink, or plastic bag around clean bedding is "doing your bit to save the planet" is in most cases illusory, as BA will be managing waste responsibly. The problem of waste in the oceans is principally a symptom of the lower availability of infrastructure in the developing world, where in the first place plastic is used (to take one example) to bottle clean drinking water, creating the waste, and where that waste ends up in watercourses in significant quantities.
So actually that is the problem to solve, but noting also that Malaysia (to take a developing world example I know well) is already limiting single use plastics led by pressure from the younger population. But this is moving into omni territory - my conclusion in terms of whether BA are doing the right thing by using plastic bags is that in all probability they are, but as with pretty much every large organisation on the planet they will be looking to do more.