There is no such thing as “their [Americans’] own environment”. “America” is an arbitrary distinction. Environmentalism doesn’t care where international boundaries are drawn, or how many sovereign nations comprise a particular area. America is also far too large to argue that it consists of one environmental zone of concern (to coin a phrase). A person living a comparatively simple and impoverished life moves from Point A to Point B, improves their standard of living, changes their lifestyle, and in the process increases their carbon footprint. It doesn’t matter whether or not it was immigration. If Mexico became legally part of the US tomorrow, nothing would change with regards to the issue cited in the OP other than the fact that they wouldn’t be labeled “immigrants” anymore.
I thought my hypothetical was pretty simple – pretend that, instead of the USA, we’re talking about a subnational region. Would you then expect environmentalists to take a position on inter-regional migration? Likely not, hence, one shouldn’t expect them to take a position on immigration either.