Absolutely! Unaffiliated voters can vote in the NJ Primary. No requirements at all except that you are registered to vote. You just declare your party affiliation once you are at you polling place. Here is the
press release clarifying the whole thing from the NJ AG's Office:
"New Jersey’s primary election law allows unaffiliated voters – those registered voters who never affiliated with the Republican or Democratic parties -- to choose a party on Primary Day and vote in the primary. "
By the way, if you aren't sure whether you are unaffiliated you can check out your status
here.
And here is some other helpful on
primary voting info from the League of Women Voters of NJ.