I summoned a zombie that could break doors and had it chase me. The zombie then broke down the door which made wooden door sounds. A villager was also tested and could open the copper door. This appears to be unintended behavior since the metal copper door isn't like the metal iron door. Also the copper door is categorized under the wooden doors and axe minable tags as of the time of this bug report.
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Relate to MCPE-176431

Confirmed