Can't add tags

I can’t edit my tags.
Relatively new site.

I accidentally added a tag named ‘tag1 tag2’ to a post because I thought spaces were delimiters. From that moment when I add tags (e.g. ‘tag1,tag3’) when editing a post;

– they show up on that edit page, nicely separated ‘tag1’ and ‘tag3’ with the red delete crosses in front. I update (save) the page.
– if I then go to ‘all posts’ or visit the page, or look in the tag cloud, that page has the ‘tag1 tag2’ tag again.

I can remove the ‘tag1 tag2’ tag so that I have none (did that for all pages, didn’t help).
I cannot add a ‘tag3’ to ‘tag1 tag2’ -> same incorrect behavior.
If I add a new page with a new tag -> same incorrect behavior.

Disabling plugins (only Akismet and Youst Google analytics) or switching to the 2015 theme does not help.

I’m in early testing and not afrid to use SQL, so if I need to inspect or update anything in the DB, that’s fine.

FWIW: http://www.planbvoornederland.nl/blog/