This may be long...I've got lots of questions!

I know there are many denominations represented at ChristiansUnite, and many different opinions on church music. I am not trying to offend anyone by what I say here, nor am I looking for folks to agree with me. I just want feedback on the subject of worship, what it means, what is important, how it should be carried out, etc. Scripture references are always welcomed!

My family is currently attending a church that is very involved in modern styles. I'll admit, my preferences in music are deeply traditional, and I am uncomfortable with the song service. I have been told that the style does not matter as long as you are worshipping God at heart, and of course, I'm not the one being praised; I try to keep this in mind whenever the congregation or college group is fellowshipping. But it hurts. There are rarely any hymns, unless they have been twisted with modern rhythms and hip, drawn-out additions. I just cannot seem to be a part of this movement to "open your mind and sway to the music".
I had a chance to investigate the doctrine of worship in another church; they spoke against the tendency of today's churches to embrace the culture around them and fill their services with jazzy, diluted stuff to attract the "younger generation". They promoted a more traditional theme which revered the awesomeness of God, regardless of the feel-good style that pervades other congregations. In a nutshell, they basically described the purity of worship music I've been longing for.
Just when I was feeling "welcomed home", they went on to say that
any worship other than what was prescribed in the Bible is strange fire on the alter of God; they will sing only Psalms, and nothing else. They claim that hymns glorify man, not God.
This means that they will sings Martin Luther's "God is my refuge and my strength", but not "A Mighty Fortress is our God"! They share the same tune. One is a Psalm; another is the boasting of man.

I have never heard of a church that refused to sing hymns because they were
too worldly. Generally, the excuse is the opposite. "People don't like boring hymns any more. Its outdated." Etc.
These are both Reformed churches, in the same general area.
And the FUNNIEST thing about it (heehee!) is that...
In the "modern" church, many of their new-style songs are based on the Psalms. I'm sure you folks have heard them. "Create in me a clean heart, oh God, and renew a right spirit within me...". "You are God in Heaven, and here am I on earth...so I'll let my words be few..."
If the song director of the modern church came to the strict church, he wouldn't be tolerated. He sings New Style. They sing from the Psalter. But its the same Psalm!!! (Okay, done joking.)

Now I am confused. I don't like New Style, but I've convinced myself that my preferences don't matter (much) as long as the music glorifies God. I love the people, and if they are truly praising God with this music, I can too. But what if it really is "strange fire on the alter"? The stricter church cites several occasions when people
thought they were worshipping God, and really meant it in their hearts, but did not obey the laws set for worship; they were punished. I.e., David's friend Uzzah who touched the ark. The feasters in King Hezekiah's day who came to the holy meal without proper cleansing. Cain's unworthy sacrifice. I know these are all Old Covenant examples; but do we have similar rules today? Is there a way we ought to be worshipping God as New Covenant believers? If we stray from the standards laid down for us, are we sinning, and is our praise a stench in God's nostrils?
We are told in A.D. that we must sing Psalms, share communion, etc. Are we under judgement because so few of us "greet one another with the holy kiss"? Are we condemned because so many churches have added things to the bare rules of Christian worship?
What is the line between our freedom in Christ, and disobedience to God? This opens up another avenue of discussion: have we forgotten what it is to "fear the Lord"? Have we become too familiar? And when does "God-fearing" become "legalism"?
Puzzled, troubled and a little amused,
~Joy