Hmm – I found the reason for this behavior. It is this Plug-in
Google Analytics for WordPress by MonsterInsights
They just released a new version
6.0.15, March 7, 2017
Fixed: Issue with translation string numbering in the disabled user group frontend template.
Fixed: Resolved issue that caused issue with lightbox-style redirects.
Fixed: Issue where admin pages had JS issues from mis-ordered JS files.
This does fix this strange jumping-to-the-top behaviour when you select a Drop-Down-Select-Menu.
But now there is a NEW PROBLEM. Suddenly ALL bottons in the header of the homepage (when not yet logged in) just dont work.
I have disabled the Plug-in for the time being and wrote a bug report.
With it deactivated, all runs smooth again on my site.
Maybe this is interesting for you to know, because I bet MANY are using this plug-in.
Regards
Andreas