As others have said, Christianity is such a broad spectrum these days and the term evangelical is used and mis-used so widely that it's impossible to say how this particular Christian or church would feel about the issue.
The Bible does advise Christians not to marry non-Christians. It doesn't specifically say don't date them but then dating isn't mentioned in the Bible per se. However, it doesn't forbid it and advice is given for managing mixed faith relationships too. This to me (like most of the advice in the Bible) makes sense - I think it's harder to be married to someone who doesn't share your faith.
Even a strict reading of the Bible allows for divorce and remarriage in the case of adultery by the other person or desertion of a Christian by a non-believer. Many interpret it much less strictly. Most CofE churches will marry a divorced couple as long as they weren't affair partners who broke up a marriage and the divorce isn't recent.
The whole man as head of the household from Ephesians 5 is in my opinion massively misinterpreted and doesn't say what people think it says at all. Yes it says the wife should submit to her husband but it also says the husband should submit to his wife. More than that, it says he should put his wife first at all times and be willing to die for her. It's a partnership where each person puts the other's needs before their own - not a misogynistic dictatorship. It also only applies to marriages and not to dating or to other male-female interactions.
Personally, as a Christian, I made the decision not to date non-Christians after my divorce from an agnostic due to his repeated adultery. I was single for many years due to enforcing this rule but I felt sticking to my convictions was more important. I have now been with my partner for two years and we plan to marry.
Other people, as you've seen, would be willing to date an agnostic, which is what you seem to be.
If you really like this guy, I'd encourage you to explore what Christianity means in more detail. That exploration might lead to you coming to faith, in which case the problem disappears. Or it might lead to you understanding him better and being able to make an informed decision about the challenges you might face. Or it might lead to you deciding a Christian way of life is not for you.