This report describes this bug only for 1.13(+).
See MC-125157 for the same bug in 1.12.2, whose cause appears to be unrelated to this report since it appeared later than this bug.
The player heads in the spectator mode GUI are not using the skin textures.
/team add test
/team join test @s
Spectator menu does no longer show skins (up to 1.12.2)