Yes, but they don’t endorse the position that God is essentially hate. (Anyway, I am aware of no Christian anywhere, at any time, who has ever endorsed that, though I’m hardly omniscient on the topic. 
And I fully and entirely expect that no Christian anywhere has ever done so.)
This leads to an important comparison, though (which I’ve often brought up in other threads).
God can do wrath without being essentially wrath; everyone admits this (except maybe some people who refuse to acknowledge that God can do wrath at all. But I don’t know any such Christians who do. Even the ultra-universalists here on the forum all acknowledge, so far as I’ve ever read, that God can and does or at least did do wrath.)
Calvinists, for the most part (there may be some who profess that God is essentially love, as I have heard Augustine did), would say similarly that God can do love without being essentially love.
When God can do an action without being essentially that action, then there is no incoherency in also claiming that God may either cease doing this action toward an object or never does that action toward some object. Everyone, including all Calvs and Arms, believes that God can and does stop doing wrath to at least some people (to those He successfully saves from sin, for example), and that God never does wrath to at least some persons (to unfallen angels, for example.)
But if God is essentially an action, then God cannot cease doing that action toward an object without ceasing to exist as God. To borrow an uncontroversial example from Luke earlier: if God is essentially “being” (in active existence–and I’ll have a lot more to say about that later in another thread ), then God cannot cease actively “being” toward an object without ceasing to exist.
This is obviously the significant point to God being essentially love, or not. If God is essentially love, then even if He does wrath toward a person even that wrath must be primarily an expression of love toward the person with a goal of accomplishing love toward the person sooner or later. He may stop doing wrath toward the person, but He cannot stop doing love to the person and still exist as God. (Nor can God cease to exist as God and begin existing as something only not-God instead; that isn’t something the ground of all existence can do, it would be contradictory to claim so.)
On the other hand, if God is not essentially love; if love is only one of many non-essential characteristics of God, or if (somehow) love is even merely an essential characteristic of God but isn’t what God essentially is in God’s own inherent self-existence?–then God could stop doing love toward a person (Arm theology broadly speaking with variants) or never do love toward a person at all (Calv theology broadly speaking with variants, some of which would involve God accidentally doing love to the non-elect as part of an unavoidable inadvertence for example, which how they would interpret “sending sun and rain on the good and evil alike” and letting the tares grow up with the wheat). In either case, a punishment of God could then be hopelessly final for a sinner in any of various ways (annihilation, eternal direct torment, abandoning the sinner to their fate, etc.)
But if God is essentially love instead, then there could be no hopeless punishment from God toward any sinner, nor would God ever abandon the sinner.
Calvinists are typically more aware of this point than Arminians, in my experience; although when pressed I’ve seen some Arms deny God to be essentially love in order to keep the doctrine of some kind of hopeless punishment from God instead. (I recall at least one time this happened while I was watching a discussion between Arms and Calvs, when the Calvs pounced quite rightly on the acknowledgment–since this immediately contravened the typical Arm grounds for affirming that God acts in saving love toward all sinners instead of only to a chosen elect!)
Sorry, I knew what you meant by reading things back into, but I honestly didn’t & still don’t know where I’ve done that?
(LOL!)