Permission for anonymous user I got custom registration form under /user/register URL but anonymous user gets denied access what type of permissions should I set.
 I tried:

 requirements:
   _permission: 'access content'


and 

requirements:
   _permission: 'none'


or I deleted it completly but it didn't help.
'access content' should be good in general, check it under "people/permissions" to seem if also anonymous users have right to "access content". 
You can also declare:

_access: 'TRUE'


In this case you don't need the permission part, this one should definitely work!