Do you think MBTI personality types influences who you get on with?

Yes, I do think one's temperament influences who they get on with. As for the MBTI label, the effect is not as powerful as you may think, as no one fits any one MBTI type to a T and everyone has different life experiences.

In regards to Myers-Briggs, the letters mean virtually nothing by themselves. They only tell you the Jungian cognitive functions a type has. ISTJ and ENFP have the exact same cognitive functions, but in the reverse order. Click on the link for a more detailed description of how this manifest.
https://answers.yahoo.com/question/index?qid=20141204125151AA0REhU

ISTJ and ESTP have their preferences in the same order, but in the opposite orientation, so therefore have completely different functions. ISTJ has Si-Te-Fi-Ne, while ESTP has Se-Ti-Fe-Ni.

ISTJs have internal, subjective sensing (Si), seeking depth of sensation. Their minds act sort of like a library, storing the tangible, concrete aspects of their experiences for precise retrieval. They are susceptible to being nostalgic and sentimental. ESTPs have external, objective sensing (Se), seeking breath of sensation. Their minds want what their bodies want. They gravitate toward anything in the material world that pleases the senses in the moment. They are more aware of their real time sensations. Se deals with sensations themselves, unlike Si, which has to do with the impressions of sensations. Energetic Se wants variety, tranquil Si wants stability.

ISTJs have external, objective thinking (Te), being concerned with the breath of thinking. They are concerned with established facts and tried-and-true methodologies of logic. Te is all about empirical reasoning, proof, and evidence. ESTPs have internal, subjective thinking (Ti), being concerned with the depth of thinking. They are concerned with logical consistency and systems. Ti, like all introverted functions, is not connected to the outside world. It is experimental, which is partially why an ESTP may seem reckless. The military-like Te influenced mind works like a checklist, while the architectural Ti influenced mind works like a blueprint. Ti is concerned with pure logic, while Te is concerned with effectively organized logistics. Ti uses pure deductive reasoning. "If A=B, and B=C, and C=D, and... then A=Z," thinks Ti. Unlike Ti, which is concerned with the intricacies of why a solution works, Te cares only that it works at all. While he cares little for pure abstractions, the improvising ESTP loves testable, doable theories. The risk-adverse ISTJ doesn't like theories. He prefers to play it safe and stick with what is already known.

ISTJs have internal, subjective feeling (Fi), and experience the depth of feeling. They are more concerned with morality and emotional integrity. ESTPs have external, objective feeling (Fe), and experience the breath of feeling. They are more concerned with ethics and social harmony. ESTPs can feel a pressure given off when a group of people that are, for instance, tense. However, whether or not they let that vibe actually disturb them personally is up to them. They posses an intuitive (non-MBTI) understanding of the mood of an atmosphere.

ISTJs have external, objective intuition (Ne), seeking the breath of intuition. Ne is concerned with that which is objectively not present in an environment at any given moment. It is concerned with possibilities and ideas. ESTPs have internal, subjective intuition, seeking the depth of intuition. Ni is concerned with associations and symbols. Ne conceptualizes a multitude of theories from a single idea. Ni sees patterns and relationships between ideas. It reads in between the lines of situations, creating underlying essences of experiences.

ISTJ: dominant Si, auxiliary Te, tertiary Fi, inferior Ne
ESTP: dominant Se, auxiliary Ti, tertiary Fe, inferior Ni
- dominant and auxiliary functions are strong, and tertiary and inferior functions are relatively weak
ESTP (and ESFP): https://answers.yahoo.com/question/index?qid=20140701172247AAXkGik

ENFJ has all the same cognitive functions as ESTP, just in a different order.
https://answers.yahoo.com/question/index?qid=20140417121633AAuufp1

ESTJ has all the same cognitive functions as ISTJ, just in a slightly different order.

ISTJ and INTJ share auxiliary Te and tertiary Fi. So both externalize thinking and internalize feeling. Although they may behave similarly at times, they have extremely different inner worlds. ISTJs' Si inner worlds consist of realistic, detailed memories and sentiments, from which elaborate mental maps can be drawn out for familiarization and security. INTJs' Ni inner worlds consist of pure notional imagination, from which insights and foresights are gained through associations and symbolic patterns. Both their Fi inner worlds of pure emotion, morals, and personal values are somewhat suppressed and fairly weak, since their Fi is in the tertiary position. ISTJs have difficulty thinking outside the box, due to inferior Ne. INTJs have difficulty in purely engaging in their five senses, due to inferior Se.

An ISTJ may admire the auxiliary Ne of the INTP. However, the Si inner world of INTP is moderately suppressed. They instead have a powerful Ti inner world, which consist of complex logical deductions, mechanical frameworks, and structurally arranged principles, from which synthesized knowledge can come about.
INTP: https://answers.yahoo.com/question/index?qid=20141011060135AAOnHXH

General descriptions: https://answers.yahoo.com/question/index?qid=20141213031812AAQdQBz

Maybe, PS maybe not PPS maybe yes PPS maybe N.O.PPPS maybe PPPPS it depends.