Will this split lead to local tourist agencies to lobby their governments.
Yes particularly in France and Italy. Protests in many resorts and mountain towns. Legal moves by regional governments to try to overturn national decisions. Austrian areas seem more sanguine about it and focussed on the Xmas Eve opening for Austrians and Jan 7 for everyone else. Also see: https://www.bloomberg.com/news/articles/2020-12-09/french-ski-resorts-challenge-macron-in-a-bid-to-save-christmas