Sure, you are free to also NOT date her, but I'd be more concerned with the attractedness and relatableness than how many points does she adhere to.
I think this is a recipie for disaster. A nonchalant attitude toward major doctrinal differences will only cause major disagreement at later points and possibly resentment and strife. If, and that's if, she is staunch in her views and unwilling to yield, I would avoid becoming involved any further. Agreement in doctrine is vital because it will dictate what your children are taught.
Further, I wholeheartedly disagree with your assessment that a general response in the negative to the stated question constitutes legalism. Legalism, as I understand it, is the creation of non-Scriptural burdens for other people. In practice, it is forbidding as sin things which we are free to do.
No one is proposing this. First, it wouldn't be "legalism" for him to obey his own conscience if his conscience dictates that it would be wrong for him to date an Arminian. We are not to ignore our own consciences. Further, he wouldn't be denouncing the practice as a whole as sin, in that anyone, including himself, who does this is sinning. That would be legalism. He would merely be determining that it's a bad idea.
Practically speaking, it is a bad idea. It's a recipie for a troubled marriage based around disagreement over some of the fundamental doctrines of the Bible, i.e. soteriology.
If she changes and becomes a Calvinist, as you did, then wonderful. If she doesn't, then problems are likely, not necessarily, to arise.