You shouldn't have to reconcile your competitive nature with also being an INFJ. INFJ's are just as capable of being competitive as any other MBTI type. If anything INFJ's make some of the most fierce competitors out there, especially in combat sports. Here's why:
I: Our thoughts are focused inward which is a trait that many world level athletes have. People like Michael Phelps for example don't compare themselves to others, they compare themselves to themselves. Introverts usually wake up in the morning and say "what can I do to improve myself". This is a competitive trait.
N: Setting goals, seeing paths and possible outcomes. iNtuitives are very good at setting goals and working to achieve those goals. They can see the end result clearly before it has actualized itself, so it's very easy for them to gradually turn their goals into reality. Another competitive trait.
F: This is the most competitive trait in MBTI. Boxers, wrestlers, kick boxers, football players, etc. are usually extremely emotional people. Extroverted feelers have the ability to extract emotions from the people who surround them, they extract even more emotions from the people they love. For example, an extroverted feeler can become a very competitive person because he/she wants to make his loved ones proud or wants to make them happy by giving them a better life. This is a very competitive trait.
J: Organizing thoughts. Getting up in the morning and making a list of goals is a total J activity. People who organize their thoughts are very likely to be strong competitors.
I have INFJ tendencies and I am also super competitive.