What someone identifies as is their business and their business alone. You don't have to like it, you don't have to understand it, and you don't even have to attempt to understand it, but you should respect the person as you would anyone else nonetheless.
Who someone is or is not attracted to is their business and their business alone, as long as everyone in the equation is a human consenting adult.
Gender and sex are not the same thing. You don't check the genitalia of every person you meet to ensure that they're male or female, so you shouldn't arbitrarily change your standards for trans people.
Gender is a social construct, it's not binary, and definitions of gender are not set in stone. While "male" and "female" gender roles are pretty universal in every culture, what constitutes masculinity and femininity (and their respective gender roles) changes over time, and plenty of cultures throughout history have had some sort of third gender (see two-spirited Native Americans).
Being masculine does not make you male, and being feminine does not make you female; drag queens identify as male, but present as female. Neither masculinity nor femininity is inherently positive or negative. While most people fall on the masculine-feminine spectrum, some don't, and others actively reject it; they may choose to identify as non-binary, and there's absolutely nothing wrong with that.