Lutherans register as mainstream on my radar. Your particular group may not; I have no basis for saying.
Everything I know about Lutherans I learned from Garrison Keillor.
Basically there are 2 large and one medium sized Lutheran church bodies along with a bunch of smaller ones.
The large ones are the Evangelical Lutheran Church in America (ELCA) and the Lutheran Church Missouri Synod (LCMS). The medium sized body is the Wisconsin Evangelical Lutheran Synod (WELS).
If you want to look at it from a liberal to conservative spectrum the ELCA is by far the most liberal, has women pastors, allows homosexuals to be pastors, takes no position on abortion but most of the top level clergy is pro-choice., allows gay marriage. They also serve communion to all baptized Christians.
That having been said it should be noted that the ELCA allows individual churches to use discretion on these views. So you could very well meet an ELCA pastor who would completely refuse to conduct a homosexual wedding or you could find a ELCA church that refuses to hire a pastor because he is homosexual. So just the national organization allows it doesn't mean every church goes along with it.
The LCMS would be in the middle but far closer to the WELS than the ELCA. Only males can be pastors, against abortion, no gay marriage or homosexual pastors. (I'm personally of the belief that the policy on homosexual pastors should be that of what the ELCA used to be which is requiring them to be celibate.) They also practice closed communion which means somewhat within pastorial discretion a person has to affirm that they hold to the same doctrinal beliefs as the church to take communion.
WELS takes things a step further than the LCMS in that women are not even allowed a vote in church meetings. They also tell their followers not to pray with Christians outside of their church. There are some minor theological differences about God's calling into lay church offices that don't really impact greatly the way the church runs.
For a long time the LCMS and WELS had what is called "altar/pulpit fellowship" which is basically a recognition that the two churches believed the same things and therefore could exchange pastors and people could commune at the other church. The WELS however broke the altar/pulpit fellowship because the LCMS engaged in talks with one of the predecessor church
A thing you have to recognize about the conservative Lutheran churches is that there is a constant fear of "unionism". Unionism is the combining of two conflicting belief systems into one. So what orthodox Lutherans fear is that they will lose the doctrine which they consider to be truth by being too cozy with Christians that are not in their church body. This makes conservative Lutherans kind of like Roman Catholics in this way and something that differentiates them from most protestant churches and the so called "Evangelicals". Lutherans might have many of the same conservative beliefs on social issues as they do, but they generally don't want to get too cozy with them at the same time.
The smaller Lutheran churches run the gambit. Some the larger small churches are breakaways from the ELCA who felt the ELCA was too liberal but the LCMS too conservative. There are also some that broke away from the WELS because they didn't feel the WELS broke the alter/pulpit fellowship with the LCMS fast enough.