Well I think there's need of communication. Keeping in contact with past partners isn't completely wrong unless they are cheating behind your back. Maybe they don't want to tell you cause they feel you might misunderstand? A person can change with time, so I would say just talk it out.
Also, this sounds so similar to the plot of Love me Doctor (it's a BL). You might check it out maybe that will answers some of your questions.
Definitely communicate with them. They might be worried that you’ll judge them or hate them for it, so just be as open and understanding as possible. Communicate how it makes you feel honestly.
And also, I know this can be awkward to talk about but you definitely want to make sure they’ve been tested for STDs and are clean before engaging in anything sexual with them. In can be an uncomfortable and delicate conversation, but your health and safety comes first.
For me, it's okay if that person have a history.
I mean yeah, people can change. But if I found out that he/she did the same shit behind my back when we're supposed to be going out, I would immediately leave his/her ass. I'm totally a vanilla type of person, I don't wanna share them with another.
And keeping in contact with the ex..?
I would trust him/her.
I just don't trust the ex.
Just imagine that there's a person who wants to date you and they seem genuine but this person used to live a promiscuous lifestyle that you didn't know about, and you find out they have baggages from that old life (keeping in contact with people they've slept with) that they're keeping from you, what is your take on this?