Legal aliens and the Second Amendment

The previous post discussed the issue of Second Amendment rights and illegal aliens. but what about non-citizens who are legally in the country? Here's a post on Volokh discussing this issue:

The Second Amendment / illegal alien decision discussed in the post below reminds me of a broader question — do noncitizens who are legally present in the U.S. have Second Amendment rights?

1. Federal law generally bars gun possession by noncitizens who are here under a nonimmigrant visa. Some state laws go further and ban all possession by noncitizens, including by permanent residents. The law of Guam likewise bans all possession by noncitizens, and because federal statutes extend the Bill of Rights to Guam, the Guam law could be challenged even without reaching the question whether the Second Amendment is incorporated against the states.

Generally speaking most constitutional rights have been extended (at least where criminal punishment, as opposed to the threat of deportation, is involved) to legal aliens. Should this apply to the Second Amendment? The reasoning in the illegal alien opinion seems to potentially apply to legal aliens as well, though that's not clear.
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Read the rest here.