Redbeds are a broad catagory of sedimentary rocks that contain a small amout of hematite that is enough to color them red. They are especially abundant from the Pennsylvanian and Permian eras. The sediments can range from fine grained shales to coarse conglometates. The famous Red Rocks Ampitheater near Denver is built in the Fountain Formation, a red-bed.

Some of the magnetic minerals are aligned to the geomagnetic field at the time of deposition. Some of the magnetic minerals are created during burial and align to the magnetic field of that period of their long lives.

They hold really nice paleomagnetic signals so they have been used extensively in reconstructing the position of the paleo geomagnetic north pole (pole wander paths). This can then be used to determine the position of the tectonic plates through time. Each step of this deductive process has it's difficulties, assumptions, and sources of error.

Modern red clays should contain enough magnetic minerals to be weakly magnetic and act as a lodestone.

You'd be surprised at the magnetic strength of ordinary rocks. I've encountered many outcrops with strong enough magnetism to deflect a compass, and not just magnetite deposits or Banded Iron Formations. Granite outcrops at high elevations get struck by lighting and that charge is enough to strongly magnetize the rock.