How do I use non-admin theme for page containing node form?
Well, the issue was related to the bug in metatag module, it was in version 8.x-1.0-beta11. 

It caused break of my routes when they ended with /add. It was trying to handle prefix of path as entity type, so my routes worked fine only if I had _node_operation_route: TRUE in route options. But if this option is set _admin_route: TRUE is added by core.

I updated metatag module to the latest version (8.x-1.0 currently) and found they've added check for existing entity type, so I'm not forced to use _node_operation_route: TRUE anymore and I'm able to output custom routes in a default site theme.