So most members of the LDS church see themselves (or at very least their church) as highly evangelical. Certainly the requirement to preach the gospel is a key component of our doctrine. And many people outside the church who know our young, name-tag wearing missionary force have a keen sense of the evangelical mission of the church.
Oddly enough, there seems to be some dissonance between how we and our immediate sphere of influence perceive us, and how most of the world perceives us. In a recent meeting with Elder L. Tom Perry, one of the most senior leaders in the church, leaders in Minnesota learned that the church has studied the question and that most people have little or no perception of who we are - their exposure has been very limited and there are plenty of mis-perceptions about our beliefs.
A recent conversation with an acquaintance provided anecdotal support for this conclusion; she told me that "the difference between Mormons and 'mainstream Christianity' is that we are not Evangelical enough", and that we allowed others to define us. This assessment of the church came across in spite of the fact that the person making it had both received a Book of Mormon from a member of the church, and had received a visit from missionaries on her doorstep. She knows that we have an evangelical bent to us, and yet her perception is that it is not enough.
I think many members of the church are so careful to not offend, or to come across as pushy, or afraid to be perceived as preachy, that we err to the other extreme. What we don't realize is, that by not talking openly about what we believe, we may actually come across as closed off, secretive, or even arrogant.
So, while our doctrine is that the duty to preach the Gospel (evangelize) is key and central to our faith, we have a long way to go in becoming who we ought to be.
So, your Mormon neighbor does want you to ask about their faith. They want to have a chance to invite you to see their church and meet other members. Since you're curious any way, do them a favor and ask. And they'll still be your friend even if you decide not to pursue it any further than that.
