Which trait is common to both science and pseudoscience? Both offer an explanation. Both are based on facts. Both are based on beliefs. Both change with time.

Both change with time.

Explanation:

Scientific theory is based on complex methods of observation, deduction and experimentation.  The resulting findings are usually tested and peer extensively peer-reviewed before being regarded as factual information. Science often changes with new data and experimentation.

Pseudoscience, uses relationships between data and observed phenomena to draw conclusions. This often involves compelling assumptions, and anecdotal data without the need for external review or validation.

Both may change over time, as society's approach to new information and phenomena evolve.