The unpleasant fact of climate change will sooner or later force us to change the way we live. This applies generically to humans as consumers, not only to celebrities.
As long as we keep this point in mind, I don't think it's a distraction to talk about what specific life-style changes are appropriate now, as well as talking about what government policy changes are appropriate.
For the average western consumer today, a reduction in meat consumption is a good idea for health reasons as well as for the environment. However, I'm not convinced that a pure vegan diet is appropriate for all humans, let alone for cats or dogs.
I think Lewis Hamilton is over-reacting to one aspect of the climate change problem, while under-reacting to other aspects... Which is still much better than denying that there's a problem.