I'd like to share with you a passage from as book I am currently reading. It's called God-Centered Evangelism by R. B. Kuiper. While Kuiper does not come out and say the two can't work together under any circumstance, he does warn his readers that it is indeed a serious issue that must be considered:

The most serious obstacle to unrestricted co-operation remains to be considered. There are among them certain doctrinal differences which affect in a direct way the presentation of the gospel and are by no means insignificant. Here the difference between the Reformed faith and the faith of the Arminian must be named. They agree fully that the divine offer of salvation is perfectly sincere in the case of all to whom it comes and that nothing would please God more than the acceptance of that offer by all in faith. They also agree that the sinner is obligated to believe in Christ and that, in case he fails to meet that obligation, he will perish through his own fault, and not through any fault on the part of God.

Yet there are appreciable differences. The Arminian will tell each sinner that God designed by the death of His Son to save him; the Calvinist will insist that Paul never once addressed a sinner thus, and that he could not have done it because this would have implied that mere man could thwart the plan of the Almighty. The Arminian will tell unregenerate man that he has the ability to believe in Christ and that, if he exercises that ability of his own free volition, he will be born again; the Calvinist will insist that unregenerate man, dead in trespasses and sins as he is (Eph. 2:1), will not and cannot come to Christ in faith except God draw him by the irresistible and regenerating grace of the Holy Spirit (John 6:44). Let no one term these differences minor or ridicule them as mere hair-splitting.

On this matter Benjamin B. Warfield says in The Plan of Salvation: "The issue is indeed a fundamental one, and it is closely drawn. Is it God the Lord that saves us, or is it we ourselves? And does God the Lord save us, or does he merely open the way to salvation and leave it, according to our choice, to walk in ir or not? The parting of the ways is the old parting of the ways between Christianity and autosoterism."

True godliness is a sincere feeling which loves God as Father as much as it fears and reverences Him as Lord, embraces His righteousness, and dreads offending Him worse than death~ Calvin