Fulltext stoplist replication
stoplist can't be replicated but there is one ugly way to do it. Words in Stop lists are stored in sys.fulltext_stopwords . Using linked server you can query this table and compare it on secondary server . If there are any changes then run alter command on secondary to add\remove those changes from stoplist.

ALTER FULLTEXT STOPLIST YourStopLIstName ADD 'en' LANGUAGE 'Spanish';

Can be setup as recurring job. Not a decent method but should work fine.