Great answer! I agree that correct doctrine is not absolutely essential for one to be saved, with the possible exception that it must at least present Jesus as Savior, Who died for your sins to purchase forgiveness and cleansing from sin, and Who rose again for your justification. Most Christians start off as Arminians, because that is the prevailing doctrinal stance of most Evangelical Christians. I know I did, and it was only after years of reading scripture, asking questions, and waiting on the Lord to quicken His Word to my heart and mind, that I began to see that what I thought was right didn't answer many questions I found myself asking, and I kept running into the idea that God was Sovereign over all, and that He was not under any obligation to save anyone. Further discussions, debates, and scripture searching led me to embrace the Calvinist position, even though I didn't know that was what it was at the time. I was not introduced to Calvinism by Calvinists, but by God Himself. Calvinism is just a convenient handle to hang on what is, in reality, the Truth of God's Word.
I don't believe that Arminians are lost, unless they willfully refuse to hear the Truth. Even then, I am not willing write them off, but just see them as deceived and in need of God's enlightenment. That's His department, not mine, other than I am posting and participating in discussions to clearly uphold and define the Truth, not to condemn, but to plant seeds, to maybe water those seeds, but it is God Who will give the increase.