My Answer –
Muslims believe that if you are not a Muslim you are not going to heaven. You can even ask questions about whether most of the titled Muslims might not even be Muslims by Islamic standard.
But converting other people is not exactly a goal of Muslims. Some racist or islamophobics might mislead you with their sickness. But if you are a clear headed logical person you will see right through these people or ideas.
If a guy likes you, even if he knows he is not allowed to keep living or staying in a relation with a woman without marriage or converting her into Islam still he might date you. Following rules doesn’t happen always. Salah is a important must do yet many Muslims don’t do it regularly. But if he/she actually have faith, sometimes they might come to realizations about these. For example he might realize that according to his belief he is not going to live with you forever because for Muslims, usually they believe if you marry someone you will end up with her in heaven. So it’s not like just a life time deal, it’s a forever deal. It’s not like western culture, where you keep changing partners ultimately ending up alone when you are old. That is exactly what happens most of the time in the west. Islam is not like that.
Islam is a quite romantic religion. According to Islam, Adam got bored in heaven and when God created Eve for him, his boringness went away immediately.
So if your boyfriend have actual faith, he believes if you are not converted you two wont’ end up in heaven together. And that is probably he wants. So it’s your decision whether you are truly devoted Christian gets priority or current your boyfriend. You can even leave him and choose someone from your own religion or someone who would not impose such rules.
And before you accept the Muslim guy you should know more about Islam because you won’t be allowed to have male friend. He might want you to wear Hijab. Some of them are strict, some are flexible. You should know more about them before you accept a new religion whether you are up for it. Islam is quite an easy religion for many. But for western society some of the ideas might seem too much, like not drinking alcohol, or not having friends from opposite gender. Because according to Islamic belief, opposite gender create such attraction that is devastating toward the bond of marriage. Basically they are time bombs to the married people. So it’s essential part to keep proper distance. It’s not going to be like you are not allowed to talk with males, it’s just you wont’ be passing fun time with them once your are married. Like or not, that’s just it.