Is it normal/fair for my boyfriend of a year and a half (who has been pushing for us to attempt poly/open relationship since we started dating) to restrict me from dating my preferred sex while he can still date his preferred sex? I feel this tears at me because he encourages me to be with women, but the idea of being open is also making me attracted to men and the whole ordeal is causing some inner turmoil for me.
Is it normal? If you define "normal" as "common," then yes - this sounds like a "one penis policy" or "one dick rule," and those are relatively common. Does that make it fair or okay? No. It's not really a good benchmark for appropriate behavior to ask whether other people do it.
I think such "restrictions" in open relationships are pretty stupid - they betray a lot of assumptions on the part of the person setting them that aren't really based on reality and are pretty arbitrary. There is nothing about sex with a man that is more emotionally threatening than sex with a woman, unless you decide that it is, because you think that it is, because your perspective is warped by weird misconceptions about gender and sexuality. Your partner thinks he is keeping himself "safe" from something if you only date women - but that makes no sense. Safe from what, exactly? Those misconceptions deserve to be interrogated rather than indulged.
So now you have me, an internet advice blogger, confirming what you already know: that these relationship terms are not working for you. The problem is not you being unreasonable while your partner asks something entirely fair, reasonable, and valid. Now your job is to do something with this information. Have a chat with your partner about where this comes from and what the two of you can do to help address the real root of his feelings and fears - not by scapegoating an arbitrary trait of potential partners. And if he continues to hold that something is non-negotiable when it's really bothering you, then you have clear information about whether the terms of this relationship will work for you.