I'm Muslim and I have a boyfriend whose not of the same religion or culture as me. It took me a really long time to follow my feelings because of religion (and also he's a year younger than me - which I usually found gross, but then he happened lol). But what pushed me towards dating my him is that I met him during a time I thought I was depressed, and without him I know I wouldn't be happy right now because he's always something I look forward to - and no one can make me smile the way he does by just being there. He motivates me to do better in school, and respects my religious beliefs.
Another thing, is that times are really changing. Divorce rates are so high now, and a common reason people divorce is due to people not knowing each other well enough before getting married. Having said that, I'd never marry someone I don't know well. My mum's on her 3rd husband now because she's always been rushed into marriage as she wasn't allowed to date. So wouldn't it be better to find that one person and stick with them because you know them well enough to know they're right for you? Of course there are those who marry without dating and never divorce, but look at the percentage of such couples before you try to rebut my point.
I honestly think that in this modern day and in this society, it's almost impossible to adhere to SOME Islamic laws. For example, it's said that women can't travel alone without men, even if it's just a car ride. But imagine a working class family where the husband and wife work in different places. It would be impossible for them to go everywhere together... so clearly some things must not be as much set in stone as they were centuries ago.
Please don't come at me with criticism, because I know what I'm doing isn't very halal. But it's not completely haram as we already agreed that we wouldn't have sex until marriage, and he's considering converting as his sisters are Muslim converts. I still love my religion very much, and I also love my boyfriend.
So what I'm trying to say is: adhere to your religion, but also consider your happiness too. If you have a feeling, it must be for a reason, and suppressing those reasons will only make them worse in the end. If you do decide to date him, don't go too far with your relationship - as in don't be anymore intimate than hugging/kissing. Hopefully Allah will understand that you really like him and plan on actually going places with him, rather than a quick one night stand.
Hope this makes you feel a bit better!