Can we be both agreeable and disagreeable at the same time? Understanding the big five personality traits appears to give the promise of understanding ourselves better.  However, it is clear that our behaviour is variable, for example:

individuals may be highly agreeable (or disagreeable) in the presence of family and close friends yet be the opposite unfamiliar situations.
anxiety (neuroticism) may not be a problem in familiar situations yet be strong in unfamiliar situations.

Questions

The Big Five suggests that we behave consistently irrespective of the situation. How can this be true given the apparent differences in behaviour that exist in each situation?
How should individuals take this into account in their career choices?
There are two main theories of behaviour, trait theory and situationism.
What you are referring to is known as situationism. A doyen of trait theory was Raymond Cattell who was the father of modern personality testing (his 16PF test was a forerunner of the Big Five).  An assumption of trait theory is that individuals have inherent personality traits and will therefore behave consistently irrespective of the situation. Conversely, situationists suggest that the situation an individual finds themselves in has a significant impact on the individual's behaviour.  The extremity of the situationist argument is that individual's do not have personality traits at all and that the situation is sufficient to predict and individual's behaviour. Both trait theorists and the situationists have evidence to support their positions and I think it is generally accepted that the truth lies somewhere in the middle. To resolve the trait theory versus situationism argument are the emerging computational approaches such as cybernetics and system dynamics. Unfortunately, these emerging fields are in their infancy and nothing to report at this time.
All of the above was a long-winded and round-about way of saying that the Big Five is not perfect, but probably the best you can do just at the moment.