[SalesForce] picklist value filters in list view showing all values despite record type

Yes you will need to create a new page layout/record type if you want to give visibility to one group while hiding it from another group.

So you would have contact record type A: (original layout) then contact Record Type B: (customized layout)

You then can assign the correct layouts by record type for the profiles you wish to view the new picklist values

Actually you have two options to prevent situations as you have described. First option is to create validation rule on XYZ object that will check is value in picklist is related to record type. Follow the example:

OR( 
AND(
    RecordType.Name = 'A', 
    OR(
        ISPICKVAL(F1__c, '11'), 
        ISPICKVAL(F1__c, '12'), 
        ISPICKVAL(F1__c, '13')
    )
),
AND(
    RecordType.Name = 'B', 
    OR(
        ISPICKVAL(F1__c, '1'), 
        ISPICKVAL(F1__c, '2'), 
        ISPICKVAL(F1__c, '3')
    )
)

)

Second option is using Workflow Rule that will run everytime when user changes record type of XYZ object.

Follow the rule criteria:

ISCHANGED(RecordType)

This workflow should execute field update that will set picklist value. It is very easy to create it. During creation of workflow you should add new action, choose field update as a action type and select field to update (your picklist F1). You should be able to set this value to '-- None --'. If you want set it to first value that is related to record type, you have to create workflow rules for each record type. Each of them will be fired when user changes record type to value that is handled by workflow.