Should "gender" be required, or is there a better way to collect this information?

I believe in keeping a registration form as simple as possible so that we "grease the skids" toward conversion. Every field on our signup form is required, or else we wouldn't ask it. Here's what we have now:

  • First Name (to personalize correspondence)
  • Last Name (to verify identity in person with an ID for in-person offers)
  • Email Address (to communicate, and to serve as user ID)
  • Gender (demographic info)
  • Birthdate (to verify age for COPPA compliance, and demographic info)
  • Password (to authenticate)

I am concerned that by requiring gender, we create friction (a UX concern). I am also concerned that by making gender optional we lose some important data that Sales needs to do their job (a "business" concern), as well as lose credibility among clients and partners who might not understand the UX justification.

We considered a number of options, each with its own foible or two:

  1. Require, but include third option ("decline to state," "other," or something similar): because we send out retail information, we fear people will choose the third option more often to avoid receiving "gendered" content (which would not be the case).
  2. Leave optional, but do not list it as such: without marking fields as required or optional, we simply wouldn't give an error if they left this one unselected, but this seems less than transparent, almost a "dark pattern."
  3. List as optional: how much data will we lose? And will our clients and partners question our intelligence for not making an "obvious" requirement? Fear, uncertainty, and doubt factor largely here.
  4. Move it off registration and collect as a survey question: this guarantees we'll collect much, much less data, but gain a 12.5% simpler form.

So, what to do? Require gender? Make it optional? Something we haven't thought of?

[By the way, the gender field is currently a drop-down defaulted to "select a gender." And we understand there's a difference between sex and gender; we're more interested in how the user identifies than biological stat, hence "gender."]


UPDATE

We decided to include the question on the form, and follow @Morawski's advice and simply use binary radio buttons side-by-side (without a title). We have yet to decide if it will in fact be required in the back end (thereby returning an error if it's blank), but we will not annotate it either way.