I certainly hope that Arminians are saved and believe so because I was one for five years after I was converted, before I became Reformed in my theology. I believe that I was in a state of grace at that time.
I think that Arminianism is an extremely defective and weak theology. It has serious consequences and ramifications for the church in general and for the Christian individual in particular. Are they saved? I always like to say yes, but by a happy inconsistency. If they really believe what they say they believe, then I don’t think they would be saved.
Arminians affirm justification by faith alone, the work of Christ, and all of those orthodox things. However, if you ask them why it is that they’re saved and their neighbor isn’t, they will say that God gave grace both to them and to their neighbor but they said yes to that grace and cooperated with it while their neighbor said no and rejected it.
I say to my Arminian friends: “So, you did the good thing and your neighbor did the bad thing. You have something to boast about, but they have only sin. You have done the right thing, but they’ve done the wrong thing. Your work, in the final analysis, is the decisive factor for your being saved, whereas the bad work of your neighbor is the decisive factor for why they’re not saved.”
When I say that to my Arminian friends, to their credit, they always say, “No, I don’t believe that I’m saved on the basis of my works and that my neighbor is damned by his bad works.” They don’t believe that, but I’m telling them, “That’s what you should say if you’re going to be consistent with your theology.” Fortunately, they’re not consistent with their theology.