What happens later in the relationship when you reveal you lied about your favorite book as some weird social vetting process? It seems the insincerity would turn a lot of people off.
As someone who also hates extreme non-nuanced views, and seeks people who are thoughtful and emotionally level, I don't think I would be put off at all.
In fact I'd guess that if you really did talk with tb for a while, you would probably pick up that Ayn Rand is not a fit for the beliefs they convey.