Like you've literally only been on 2 dates and he already wants you to meet his family and go out to dinner with them.
Keep in mind 1- I really like him and have feels for him. 2.- I'd say this could be a "love at first sight thing". From the moment we met there was just a bizarre connection and it felt like we've always known each other and been together. 3- He isn't a clingy guy at all and doesn't come across as desperate in any way. If anything I can't believe this is already happening
I think it just depends on how close he is with his family, because a lot of people wait it out, and bring a special girl to their family who they see a future with-- but you did mention its been a really short time and maybe he just feels comfortable with you and wants to get the introduction over with? He could just really be a family guy and feel that its the best opportunity to have you over. However I personally would feel kind of intimidated just because if it didn't work I would feel bummed out that I met the family, as soon as you meet the family and (fortunately) if you like them, they will become kind of your family too, so it's tough in a relationship if it ends sour.
That seems really soon to me, personally. I think the families should be introduced only after the relationship is actually "official." Because then, you're actually calling each other "boyfriend/girlfriend" so it makes more sense to meet each others' families at that stage. If you've only been on two dates, I would hate to meet the family and then decide not to pursue an actual relationship with this person.
I know you said you have a strong connection which is great, but I would still want to be a bit more cautious before taking that next big step of meeting his family.