There are several ways to do it. Yes, you can convert the input_datetime’s state to a datetime object using strptime.
{{ strptime(states('input_datetime.fridge_1_filter_changedate'), '%Y-%m-%d %H:%M:%S')
+ timedelta(days=change_days) }}
The result is a datetime object.
Alternately, you can leverage the fact an input_datetime has a timestamp attribute. We can add change_days to it (in seconds) then convert the result to local time.
{{ state_attr('input_datetime.fridge_1_filter_changedate', 'timestamp')
+ timedelta(days=change_days).seconds | timestamp_local() }}
The result is a string.