The problem is you cannot marry with a non-muslim person, so he/she should accept Islam first.
I’m a muslim and as far as I know, there’s no law that forbid you to marry non-muslim. There’s many muslim clerics or saints who are marry a non-muslim in history of Islam.
But to do that, first you need to have a really strong faith so your partner in future will slowly understand and accept Islam by her/his own will. The common understanding that seems to not marry a non-muslim by many muslims because is not an easy path to have a relationship with different faith. Especially family and tradition on both side.
The most common cases about this are men muslim married a woman non-muslim. On the opposite, is very rare cases that happen in history of Islam. Some (fiqh) law by clerics forbids woman muslim to married a men non-muslim, and some allowed that with requirement the woman need to have a strong faith first.
I have many friends who’s their parents married with different religion (islam and christian, islam and shinto, islam and confucius). I admit is not an easy path than married with same religion as far I can see in my own cases, but I respect their choice…
Iran has more freedom than you think. Yes, the law about how to dress is very restricted there. But as far as I know for marriage law, Iran (Shia islam) surprisingly very flexible on that compared to other Islam sects. There’s no problem on marriage in Iran to married a non-muslim partner, even without any requirement (of course an agreement from both side men and woman is needed, even parents agreement are not needed for some Shia sects and its legal). But for sure exclusively, any muslim woman in Iran who’s not obey on how to dress properly according to Shia Islam (even she’s married with non-muslim), the punishment will severe.