Why Calvinist Christians Should Still Embrace Non-Calvinist Christians

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Calvinist or not, the fact is it's important to preach the Gospel right. What I am pretty much against is Hyper-Calvinism which is utter heresy and destroys missions. I would want to believe some people were actually chosen for salvation. Some of the best preachers in the past were Calvinists like Charles H. Spurgeon. Other Calvinist expositors in the present are Pastor John F. MacArthur and Pastor Paul David Washer to name a few.

So why do I still embrace non-Calvinist Christians? Simple- as long as they are truly converted, they are already my brothers and sisters in Christ. When they show they are truly saved like blossoming in good works while still keeping in mind they are only saved by grace through faith, they are my brethren. Pastor John F. MacArthur still honored Presbyterian minister the late Vernon McGee and Billy Sunday who weren't Calvinists either.

Here's some words from David Cloud who I know is not a Calvinist but definitely still a brother in Christ take from here:
In conclusion, I thank the Lord that there are many IFB churches that aren’t cults. Independent Fundamental Baptist isn’t a denomination; it simply identifies certain major characteristics of a type of church. It means that the church is Baptist in doctrine and polity, fundamental in its stance on separation, and independent of denominational structures such as American Baptist or Southern Baptist. 
Beyond that, IFB churches come in a wide variety of stripes, and when I find one of like mind and join it, I am not joining all IFB churches! 
I can be independent fundamental Baptist and fellowship with likeminded independent fundamental Baptist churches without being unified with the IFB churches with which I disagree. I am at liberty to speak against any IFB church or preacher that is in error. 
This is in contrast with the Southern Baptist Convention, for example, which has to maintain denominational unity. For example, four Southern Baptist leaders recently said that Calvinism should not divide the SBC. David Dockery, president of Union University, said, “I think we can come to a place where we can all work together” (Baptist Press, Aug. 6, 2012). 
Independent Baptists don’t have to make such compromises. Since there is no denominational structure to preserve and and no cooperative program to support and since we are not yoked together in any organizational sense, we can speak out on any issue and call heresy heresy and let the chips fall where they may. In this context, I can accept a Calvinist as a brother in Christ, assuming he shows evidence of knowing Christ personally, and I can appreciate him in many ways, but I don’t have to minister together with him and I don’t have to keep my mouth shut about what I am convinced is serious error. 
I personally know many IFB pastors who are humble, godly men who wouldn’t dream of taking the place of Christ in the lives of their people, who invite the people to test their lives and teaching by God’s Word, who do not lord it over the people but exercise the office of shepherd according to 1 Peter 5. I know of many IFB churches where the members wouldn’t dream of giving a mere man “unquestioning loyalty.” I personally know many IFB churches that despise Quick Prayerism and hold high standards for the pastorate.

Also one must note that it doesn't mean if one is not a Calvinist, that one is an Arminian. To understand about Arminianism it denies the original sin of man and teaches the conditional security of the believer denying that Christians will endure to the end if they are truly saved. A non-Calvinist Christian however doesn't buy such garbage.