For sure, people are allowed to whatever preferences they want. They just also have to be aware of how much they're limiting their options and be sure it's a deal-breaker for them. If it really is and they're polite about it, then there's no issue.
But I think having height as a deal-breaker in particular off as a little shallow because height in a boyfriend seems like a status symbol as well as being an attractive trait. When lots of women have the same standard (6"+ seems common) no matter their own relative height that's a little suspicious... Plus most men see a double standard, hence OPs reply about weight.
So personally I think it's a murky situation where there are plenty of women who are justified in asking about height, and plenty of men are justified in being a little salty about it.