I’m not exactly sure what’s going on here.. When you’re on the page with the anchor, it shouldn’t reload to display it.
For example, go here: http://generatepress.com/knowledgebase/install-activate-addons/
Then add: #activate to the end of the URL. It should jump down immediately.
It may be because the links have the full URL in them, which is necessary for all other pages.. Try removing the full URL and keeping the #whatever, see if it works.
If it does, you may need to create a new menu specifically for the homepage, and use this plugin to show that menu on the homepage only: https://wordpress.org/plugins/menu-swapper/