2 sides of the same coin?

Throughout my life I have encountered two different types of Christian people who want to influence my life. These two different types of people have always left me conflicted on Christianity and my own personal beliefs in life. Understand I am not judging either type instead what I am doing is simply providing a particular perspective gleaned from many years interacting with different people. I could add more disclaimers but the reality is that all of us will read this differently and some will take offense but I will write this anyways.
The first type of person who I will refer to as person A, proclaims to the world with their words and deeds “I am saved, I am forgiven, I am perfect!”. The second type of person or person B, proclaims with their words and deeds “God has saved me, God forgives me, I am not perfect”.
Now person A comes across to those who are not Christian as brash and rude; and that really does not bother them as they are unapologetic. Early in getting to know you they will ask “are you saved” and “what church do you attend” and it comes across not as “hey I want to know you as a person” but “I have to know if you are like me”. Not responding fast enough or with the right answers that they want to hear will unleash a barrage. Person B may not ever directly broach the subject of these two questions instead they may at some point invite you to attend a special function at their church or lend an attentive ear, be a friend and share their life. Their interactions with the people in their lives makes you desire to become their friend and get to know them. They can be generous to a fault but do their best not to allow others to see the extent of their charity.
Person A seems to always be railing against small specific groups of people for their particular sins; in this they are also very vocal and unapologetic; often times expressing how the country is going down hill because of particular people. Person B seems to always be helping people and making friends, they are very vocal about protecting the secular rights of other people and can look past the sins people commit to offer them love; they meet people where they are in life.
These are two very distinct points of view of what is supposed to be the same religious belief. How people who are not Christian react to them can be very different. A non Christian will encounter person A and this will establish a negative opinion of Christians and Christianity. If they encounter person B first they may have a favorable opinion and be open to learning more about Christianity until they encounter person A then their opinion may change.
So what is a person to do? Does anyone else encounter these types of people and if so how do you deal with this situation?