To answer the title of your post: Yes. I am a resident of Washington and have a New Hampshire permit. An Oregon permit is on my list of things to do.
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"Anyone feel like saluting the flag which the strutting ATF and FBI gleefully raised over the smoldering crematorium of Waco, back in April of ‘93?" -Vin Suprynowicz
Texas non-resident will only be issued to a resident of a state that issues no permits. New Mexico does qualify, but not because of their proximity. Even Hi. and Ca. issue a few permits, so those residents are not eligible in Texas.