You may want to try the Unitarian church, Annabea. They welcome Christians, but also agnostics, atheists, etc. Traditionally, they got their name because they were Christians who revered Christ but did not accept the Trinity. But over the years they have broadened out to include many non-Christians. Some churches, for example, will read from the Buddhist or Hindu or Muslim scriptures on occasion. Unitarian churches often attract married couples of different religious traditions - when a Jew and Christian marry, or maybe a Muslim and Christian.
I would recommend liberal Protestantism, also, except that you probably would find it too traditional. That's my affiliation. We have a special reverence for Jesus and for the Bible, but reserve the right to think freely, accepting this idea, rejecting that one. Liberal Protestantism exists to various degrees in most of the mainstream Protestant denominations, depending upon the local parish and the minister. Most Methodist, Congregational, Presbyterian, Episcopal, etc., are 'big tent' - that is, they welcome people of diverse opinions, but do find common ground in particular emphasis upon Christ and the scriptures. You may want to check them out. But try the Unitarians first. If you live in a large city, Ethical Culture may be another option.