Summary/overview:
Open Theism affirms classical truths about who God is and His ways. Many confuse it with Process Theology or finite godism. Perhaps they are rejecting a straw man caricature of the view. Most anti-Open Theism books wrongly assume that Calvinism is the only possible understanding of biblical Christianity (so they would use the same arguments against all Wesleyan-Arminians), or that Open Theism is Process Theology (Open Theists reject Process Thought even though there is a similarity or two).
Even classical theologians are now recognizing that strong immutability is a platonic (philosophical concept of a perfect being), Augustinian concept that limits God. The biblical revelation is that God is immutable in His character and essential being, yet can and does change in His experiences, relations, emotions, plans, knowledge, etc. (weak immutability). I Samuel 15 has an example of how God changes His mind in some situations, but does not change in other situations. Also see Hezekiah, Moses, and Jonah.
The nature of time vs eternity also requires godly philosophy and logic to resolve. Is God a timeless, 'eternal now' being (Greekish, Platonic, Augustinian= he was influenced by Greek philosophy and admitted trying to reconcile the Bible with the pagan philosophy he loved), or does He experience an endless duration of time (sequence, duration, succession) like any personal being must to think, act, feel (presentism vs eternalism)? (Rev. 1:4, 8; Ps. 90:2). He is from everlasting to everlasting, with no beginning or end. He does not experience simultaneity, or creation and incarnation would be eternal.
There are two motifs in Scripture. Some of the future is partially open/unsettled, while other aspects of the future are closed/settled. Open Theism takes both sets literally, while Calvinism/determinism takes the latter as literal and the former figuratively. We should normally take God's self-revelation literally unless the language is clearly figurative (God does not have wings/feathers). Open Theism is about the type of creation God chose (genuine freedom/relationships vs determinism). It is an open creation, not a fatalistic one.
Sovereignty does not have to mean meticulous control. God macro vs micromanages creation. He desired other give-and-take reciprocal love relationships (vs robots). This necessitated giving creatures genuine, significant freedom. This resulted in God chosing to not always get His way (omnipotence means that He can do all that is doable...He cannot create square circles too heavy to lift nor does He always use brute force to govern). God's sovereignty is providential, responsive, creative, not meticulous control.
Omniscience means that God knows all that is knowable. If the future is open, and it is, then God knows it as such (reality). He correctly distinguishes possible, actual/certain, probable, necessary (modal logic is relevant here). The past, present, and future are fundamentally different. The future is not a thing or place that one can go to or 'see'. The past is fixed and knowable, the present is reality and knowable, the future is not there yet, so to know a nothing is an impossibility. Aspects of the future that are known are brought about by God's omnicompetence/ability, not foreknowledge (try explaining simple foreknowledge without begging the question/circular reasoning; Is. 46; 48). Exhaustive foreknowledge of future free will contingencies is a logical absurdity or contradiction. It is not a deficiency in God's omniscience (cf. not creating square circles is not a limitation on God).
This is one of the bigger debates in evangelical circles. Rather than dismissing Open Theism without understanding it, perhaps someone can dialogue with more substance
Open Theism does not deny any of God's attributes. It simply is a return to a more biblical, coherent understanding of them.