Not necessarily. We believe in it, just not that what you describe as speaking or praying in tongues is actually what the Bible is talking about. We also have grave doubts about gifts of God that can be 'taught' as you yourself described, or that come about automatically after a specific event. The fact that Pentecostal style glossolalia is, as you rightly pointed out, a not uncommon ecstatic phenomenon in non-Christian religions is also a major issue. Why would, for instance, a pagan shaman be given a charism of the Holy Spirit? At the very least this suggests that there are other possible sources for the phenomenon than the one Pentecostals invariably seem to assume.
We don't then, refrain from speaking in tongues because we just don't believe in it but rather because we believe it to be a symptom of plani or prelest (Greek and Russian words respectively), or spiritual deception. Such occurs when one does not, or lacks the wisdom to, practice discernment and test if the spirits are of God and is considered very dangerous. Some of us are far more strongly opposed to the phenomenon than your post seems to suppose.
James