that's correct! the reference sequences, taxonomy, and weights all need to have matching IDs.
the plugin RESCRIPt has an action for filtering a taxonomy, so you can use that to remove IDs not in the sequences.
you will need to re-create the animal distal gut weights after doing that (and there is a script in the readytowear repository showing how to do this).
Alternatively, you could just train a full-length 16S classifier with those weights. A full-length classifier loses a little bit of accuracy vs. an amplicon specific classifier, but the different is minimal so this would be the way to go if you want to just do a quick test.
Good luck!