A person is totally able to be unselfish if they are not a deeply selfish person. People who do not harbor a deeply selfish people are able to be unselfish all of the time and not worry about any internal conflicts. Being unselfish and not deeply selfish are the same thing.
A person can be unselfish if they are not deeply selfish because if they are not considered deeply selfish then they are obviously not too selfish which makes them unselfish. There are certain levels of selfishness that can be obtained and to an extent you can be considered unselfish if you arent too selfish.
The desire to help others cannot be detached from the desire to be a person that desires to help others. The ultimate motive is selfish. There is no other true motive for helping others - no matter how deep the desire is to help, it ultimately comes from the need to see yourself as selfless.