You don't want to manually have to apply a filter, you don't want the filter to show up or you don't want your user to be able to modify the base filter?

If you don't want to have to apply it manually:

1. Go in the Modules configuration menu
2. Search for the module with Tittle = open, table = incident
3. Change the link type to List Filter and set your filter, Active is true, State is not resolved

If you don't want your user to modify the base filter:

1. Go in the Modules configuration menu
2. Search for the module with Tittle = open, table = incident
3. Change the link type to List of Records and in arguments put: &sysparm_fixed_query=active=true^state!=6

If you don't want the whole filter to show up, I'm not sure how you could do it as I'm unable to get a list view parameter in a business rule that would allow to hide Resolved incident.