The "coreness" of your stated doctrines should really be divided into two groups:
Group 1 (Requires Explanation - See Below)
- Doctrine of the Trinity
- Deity of Jesus
Group 2 (A Lot! see Methodists in particular)
The doctrines in Group 2 are actually rather narrow in scope and are rarely considered requirements outside of certain Bible Church cultures. Indeed, finding all three together would be difficult in many places.
Dispensationalism, for example, pretty much didn't exist until Darby Ryrie in the 1800s. Outside of hardcore fundamentalist Baptist or evangelical Bible churches, the actual scheme of different salvations for different time periods is fairly rare.
Millenialism, popularized by the Left Behind books and Hal Lindsay is a 20th Century thing. The Roman Catholic Church explicitly rejects Millennialism, for example.
Predestination typically is reserved for Calvinistic movements. Methodists, for example, completely reject the notion. Even "Free Will Baptists" reject Calvinistic notions.
As such, to find a church that doesn't consider anything in Group 2 to be "core" you have a whole lot of latitude - Everything from Orthodox to Roman Catholic to Methodist to Episcopalian to even liberal Baptist. These are issues that are more likely to be selectors for a church rather than against.
Group 1 Options
Group 1 is harder because the formulations are much, much more ancient.
The Doctrine of the Trinity was most famously formulated in the Nicene Creed of 325 AD - one of the most fundamental tenant of what most of the world assumes you are talking about when you say "Christian." Likewise, Jesus' Deity is something that I as an Evangelical, would say is fundamental to Scripture, but objectively can be seen to permeate the writings of Paul, John, and other 1st Century Christians. In rejecting those, I suspect one would naturally hold a much "looser" understanding of Scripture than again what most would consider "Mainstream."
As such, those are the core doctrines that would make you uncomfortable in a Roman Catholic Church, for example. (Some more liberal churches like certain Methodist or Episcopalian ones might let you pass, but that's at the congregational level, not the denomination.)
For rejection of the Trinity and the creeds, the LDS (Mormon) Church is in agreement with you. Likewise, Jesus' divinity is more nuanced. Additionally, their emphasis on feeling doctrine would make you feel at home - but make no mistake, there is a very definite Mormon Orthodoxy that might rear its head on other issues you haven't listed. Subjectively, I consider them to be highly orthopractic, meaning they are highly concerned with "right action," although not to the level of a Holiness movement church.
As a movement, however, Mormons are quite large and growing rapidly - and thus easy to find. It would be a church that would make your consideration list.
Additionally, Jehovah's Witness reject the Trinity and the notion that Jesus is God. Famously their "New World Translation" says that Jesus is a God, not the God. Again there, however, the rejection of these doctrines does not mean that they do not hold very rigidly to others.
Likewise, JW's are characterized by a radical rejection of racism, and are one of the most integrated 'churches' out there. This leads many to understand JW's as very 'tolerant,' but again, fidelity to core doctrines is rigid, and excommunication happens with some regularity if there is a perceived lack of fidelity to core teachings. Being thrown out of the very tight-knit community is a highly charged thing for JWs.
And, speaking as one who grew up in a Bible Church, I suspect you would find JW's treatment of Scripture to be downright maddening. While they do not have their own Scriptures that add to the Bible (like, say, the Mormons, and bearing in mind that the WatchTower comes closes), their translation of the Bible is considered authoritative, and certain peculiar translations that are authoritative may drive you nuts. ("I and the Father are One in Unity" I'm looking at you!)
If you are looking for a denomination that is most at home holding doctrines in general loosely, your "best" bet would probably be Unitarianism. Tom Lehrer famously joked in the 60s, "How do you get a Unitarian out of your neighborhood? Burn a Question Mark on his lawn." Unitarians explicitly reject the Trinity (hence their name) and like the Ba'hai understand all religions to have Divine Truth. Most famously Ralph Waldo Emerson was a Unitarian - and since he grew up "Christian," Unitarians are often lumped together with Christians by scholars.
That said, most Nicene Christians would reject the idea that Unitarians are Christian at all. Their rejection of such fundamental doctrines and what they would view as out and out syncretism makes them suspect to the eye of one grounded in the Scriptures. I say this not as condemnation but again, to place them in a mental model.
The 'Emerging Church' ala Brian McLaren
Here, you might also find some traction, as these seeker-friendly churches seek, in almost Agile-like Manifesto. From Brian Mclaren:
An awareness of and attempt to reach those in the changing postmodern culture.
An attempt to use technology, i.e., video, slide shows, internet.
A broader approach to worship using candles, icons, images, sounds, smells, etc.
An inclusive approach to various, sometimes contradictory belief systems.1
An emphasis on experience and feelings over absolutes.
Concentration on relationship-building over proclamation of the gospel.
Shunning stale traditionalism in worship, church seating, music, etc.
A de-emphasis on absolutes and doctrinal creeds
A re-evaluation of the place of the Christian church in society.
A re-examination of the Bible and its teachings.
A re-evaluation of traditionally-held doctrines.
A re-evaluation of the place of Christianity in the world.
Like Unitarians (only with a more modern bent), the rap is the same - they stand for so much change, so much 'people over process' that it is tempting for some Christians to ask if they stand for anything at all.