Thanks for your question.
We are NOT saying that the Holy Spirit, which is the agency through which God acts in His universe, is not active today. Indeed it is. His power and might are evident everywhere as is His activity in the world. What we are saying, if you will take the time to read the material on the site carefully, is that the charismatic gifts are not available today.
Our mindset in this is not "western - whatever"; it is based on coming to grips with what the Bible really teaches not on fake experiences and outright lies. As Jesus said, those who worship the Father must worship him in spirit AND in truth. As humans we tend to be extremists focusing either on one thing or the other and never getting it right. The balance is provided by the word of God.
You are right about the so-called "western scientific mind-set" which denies everything it cannot objectify, observe and manipulate. However, just because someone claims to have "spirit gifts" doesn't mean they are legitimately so gifted. It is one thing to make such claims and another to have the whole credibility of Christ brought into question because one is either deceived or a deliberate fake. Such are just the other end of the materialistic spectrum from the hard-nosed scientist but they are on the same spectrum. Their faith can't be sustained unless they see a materialistic outward demonstration. I believe, as you said, that the apostles were gifted spectacularly and miraculously but once that outpouring had achieved its purpose in the establishment of the church and the completion of the Bible, it ceased. Now the Bible is our guide to the activity of God in the world and in our lives. As Jesus said, "If they believe not Moses and the prophets, neither will they believe though one rose from the dead."
Have a look at this article on the Holy Spirit: The Holy Spirit (Click on the title)
God bless you,