In Roger Olson’s Arminian Theology, chp. 3, a 3d Myth is addressed: that Arminianism is neither orthodox nor evangelical. I cannot say that I have ever heard anyone say Arminians are not orthodox, but I have heard more than I care to admit say Arminians are not genuinely Protestant. Olson responds:
Do you hear Arminians accused of being unorthodox? non-Protestant? Or that they are “just barely Christians”?
First, he shows that Arminians are not Pelagian (who affirmed that humans had the natural and moral capacity to do God’s will apart from grace) and are not semi-Pelagian (which believes humans can exercise good will toward God apart from God’s special gracious assistance). Arminius repudiated Pelagius and semi-Pelagianism by affirming uniformly the absolute necessity of grace. The charge against Arminians — that they are not Protestants — stems from their rejection of absolute monergism.

Second, Olson proves through clear citations that Arminians have an orthodox (high) view of Scripture — sola scriptura. (He illustrates from Arminius, Simon Episcopius, Wesley and others.) They also have an orthodox view of God and Christ — affirming that God’s essence and existence are one and the same, and Arminius affirms the monarchy of the Father (with Athanasius, Easterns, and Westerns), a view presently up for debate as a result of the Grudem and Giles debate.
Third, Olson — and he will defend this throughout the rest of the book — argues that Arminians are Protestant. However, some want to narrow “Protestant” to monergism and contend that justification by faith can’t be held consistently without affirming monergism. Such would exclude Melanchthon, Richard Hooker, and all the Anabaptists. True, monergism is found in Luther, Zwingli, Calvin, Bucer, Cranmer and Knox — but not all Protestants held to monergism.
Arminians clearly believe in “by grace alone and by faith alone.”