I was a member of a non-denominational charistmatic influenced church years ago(which I now know is Arminian influenced, dispensational, with no binding confession of faith).
I don't ever recall there being a formal membership process at all. No new members class, no vows, not even a church roll. I now know this comes from a low view of the (visible) church also.
If there is any doubt as to membership being required to transfer, I would go through the biblical steps of seeking their permission. Difficult, but one of the biblical patterns we are called to pursue, somehow trusting God for the results.
If the church is as described and they want to block transfer (because they don't believe the doctrines of grace, covenant theology, or the Westminster Standards), I'd have to think hard what to do.
In earlier days, I would have just left without a second thought.
Post Tenebras Lux; "And God shall wipe away all tears from their eyes; and there shall be no more death, neither sorrow, nor crying, neither shall there be any more pain: for the former things are passed away." - Revelation 21:4