I actually googled this because I had the same thought. According to this source [0], the bill of rights says "People" not "Citizens" so he would have the same protections.
Second Amendment says "the right of the people", not "the right of the citizens", but I doubt Assange would be able to buy a gun in the US, even before all this.
[0] - https://www.maniatislawoffice.com/blog/2018/08/do-non-citize...