I've just been hired at a small Part 135 mob. No worries at all about being a non-citizen. They only wanted the right to work & a SS number. Even my temporary work authority pending my permanent residency is acceptable.
I think their positive attitude is down to two reasons:
1. Their most senior pilot is also in the same situation as me, and
2. Pragmatically, they've had trouble keeping up with a high movement rate into regional airlines due the Part 135 minimum experience requirements being quite competitive.
One slight hiccup: I've had to apply for 'advanced parole' to be able to leave & re-enter the US. A significant part of the company's work is to the Bahamas & Caribbean.