We have heard from a number of users who have reported an inability to apply markers to AVCHD MTS files because the .mts files were moved out of the folder structure created by the camera.
For example in this screenshot I demonstrate an MTS file that has been moved out of its original folder. Prelude can ingest this file and play it, however the Marker buttons are disabled because XMP cannot write markers for MTS files that are separated like this.
Instead it is important that the folder structure created by your AVCHD camera be maintained in its entirety. You can either copy the entire card to your computer then ingest from that, or ingest directly from the camera card and use Prelude to transfer the contents to a location on your computer.
When the entire folder structure is maintained you are able to add markers to the AVCHD clips.
If the original folder structure for your AVCHD MTS files is gone and your only option is to ingest raw MTS files you can transcode the clips using Prelude and Adobe Media Encoder by enabling the Transcode option in the Transfer Options. And if you create your own preset in AME it will appear as on option in Prelude.
The transcoded file is ingested into Prelude and you can add markers to it.