Yes! I absolutely believe you can!
From what I know about HSV-1 (and I am certainly not an expert and there are many people here who know much more than I do), it is extremely common. Anyone who has ever had a cold sore has HSV-1 and it can be transmitted through sharing lip balm, a drink or kissing if there is an active sore. I think it is much easier to transmit HSV-1 than 2.
From what I understand about HSV-2 , there is no guarantee but if you use condoms, and if he is on an antiviral like Valtrex or a generic version (suppressive therapy), and if you avoid sex during outbreaks, you have a 2% chance of contracting HSV-2. That is not nothing, but pretty tiny and IMHO, he sounds worth it.
He gave you some information that was hard to hear, but you now know also that your friend is an honest guy and really cares about you, since he disclosed this despite his embarrassment. Not everyone would do that. You guys seem to have established a basis of trust. That is pretty huge and does not seem worth throwing away because of the small odds of contracting these viruses.
I have also read that you are less at risk having sex with someone who knows they are HSV-2 positive rather than someone who is positive and does not know (and the majority of those with HSV-2 do not know!). This is because the carrier of the virus can be on suppressive therapy and knows exactly what to look for and when to avoid skin-to-skin contact. Note that because of viral shedding, it is possible to be infected with HSV-2 when he does not have an outbreak, but the odds are much lower.
It is just as you say, "so much stigma attached to this." The psychological burden of herpes (particularly genital herpes) far, far outweighs the pesky little rash cab appears as little as once in a lifetime or not at all (granted it is sometimes a bit more serious, but a completely manageable condition). By accepting him, you have the power to dispel some of this stigma. A relationships must endure much more difficult tests. Just make sure to always use condoms, avoid sex when he's having an outbreak, and make sure that if he has a cold sore on his mouth that he does not perform oral sex on you.
just going to add a few more things -
have you ever been tested to know your own herpes status?
have you both discussed other std's too and made sure you both were properly tested for all std's?
have you had your gardasil shot series? has he?
even though you picked the male gender, I'm going to assume that you are female. if you and your partner did nothing but avoid sex any time he has anything going on genitally, you'd be 90-92% likely each year NOT to contract his hsv2. if he takes daily suppressive therapy and you use condoms in addition to that, you'd have a 96-97% chance each year of NOT contracting his hsv2. very low odds over all. as for his hsv1 , if you also test negative for that, discuss together if you want to have protected oral sex or not to protect you from contracting hsv1 genitally and hsv2 orally from him.
keep asking questions!