Is there any reason to think that professional philosophers change their minds more than other people?

I suspect, and this is confirmed by experience, that professional philosophers if anything change their minds somewhat less than other people. Your early experience with philosophy is that you change your mind all the time. As a learner, every new paper or book seems to have an unassailable and persuasive argument, and you feel yourself pushed all over the place in your views (at least on topics where you are malleable because you haven't already thought much about them - which connects to my point below). But professional philosophers have had the opportunity to read, absorb, and evaluate many many points of views and accompanying arguments. If they have got that far they have probably formed, or reinforced, their own views on very many topics, and those views are correspondingly harder to alter from outside. It is surprisingly difficult to get a philosopher to change his or her mind. That's not because they are especially stubborn (though some are; and also not to be underestimated is the factor that...

If a person who calls themselves a philosopher is not concerned to stay ecological (stay green) is that person still a philosopher?

What you're asking is whether there could be a philosophical perspective that argued against 'staying green'. Of course there could be. For example, someone might think that the predicted bad effects of climate change will mainly affect people who are not yet born, and that individual may additionally reason that we owe no moral duty to people who do not yet exist. In that case they will not be motivated to stay green - they may even think staying green is a bad thing all in all, since it means some short-term sacrifice of prosperity on the part of presently existing people. A bigger point is that philosophy is incredibly broad both in subject matter and range of views: that we find a view distasteful or morally wrong does not mean it cannot be a philosophical view. In fact, to the extent that the view *we* hold has philosophical underpinnings, opposing views are guaranteed to have philosophical underpinnings available as well. Whether either view has good philosophical reasons supporting it is another...