See the document for user options yank-excluded-propertiesand yank-handled-properties. And start with the document yank: C-h f yank. He tells you:
When this command inserts text into the buffer, it honors the
`yank-handled-properties' and `yank-excluded-properties'
variables, and the `yank-handler' text property. See
`insert-for-yank-1' for details.
IOW, just tell me yanknot to insert properties like faceand font-lock-face.
See also Elisp, node manual Yanking.