Christians who do not speak in tongues are not "hostile" about modern tongues. But they understand that just as Paul had clearly stated "whether there be tongues THEY SHALL CEASE" (1 Cor 13:8), the genuine gift of supernaturally spoken LANGUAGES did cease upon the completion of Scripture, and the cessation of prophecies, tongues, and (supernatural) knowledge. Had the KJV translators consistently translated glossa/glossais as language(s) (supernaturally spoken by those who did not know them), we would not have what is known as "the Tongues Movement".
Now there are some here who believe that they speak a "prayer language" which they call "speaking in tongues". But the biblical gift of tongues is NOT a prayer language at all. It is human language clearly spoken supernaturally as we see in Acts 2. There is a verse or two in 1 Corinthians that appears to suggest a prayer language, but on closer inspection that is not what it about.
So there are a number of reasons why many genuine Christians do not accept the modern phenomenon of "tongues":
1. The doctrine postulated by Pentecostal churches is that tongues are evidence that the person speaking has become "Spirit-filled". Which means that those who do not are not Spirit-filled. Which means that there are two classes of Christians in existence, with those being Spirit-filled as spiritually superior to those not speaking in tongues.
2. Modern tongues are generally babbling, and hence called glossolalia, not glossais. Well there is no Scriptural support for such a phenomenon. Furthermore, people are being coached to speak this way, which again is not Scriptural.
3. Women are known to speak in tongues publicly in Pentecostal and Charismatic churches. This is a clear violation of God's instructions through Paul -- in this context -- that women are to keep silent in the churches (1 Cor 14:34,35).
4. Frequently gatherings where tongues are being spoken are also know to have some very disorderly behavior within the assembly. This is in violation of 1 Cor 14:40.
5. Tongues were a sign for unbelieving Jews to prove that the Gospel was of Divine origin (1 Cor 14:20-23), and therefore the miraculous manifestation of tongues was evident in the Apostolic Churches. But the time came when Paul turned away from the Jews and went to the Gentiles, and Gentiles began to predominate the churches. Thus we do not hear of tongues being spoken after the end of the first century, until the Montanists came on the scene (late 2nd century) and they were not well-regarded. It was not until the Azusa Street Revival in the early 20th century that the modern Tongues Movement began.
What needs to happen is that neither tongues-speakers nor non-tongues-speakers need to be contentious about this issue, but agree to disagree. We see in Scripture that the evidence of being Spirit-filled was for Christians to speak the Word of God boldly:
Then Peter, filled with the Holy Ghost, said unto them, Ye rulers of the people, and elders of Israel... Now when they saw the boldness of Peter and John, and perceived that they were unlearned and ignorant men, they marvelled; and they took knowledge of them, that they had been with Jesus. (Acts 4:8,13)
And when they heard that, they lifted up their voice to God with one accord, and said, Lord, thou art God, which hast made heaven, and earth, and the sea, and all that in them is:.. And when they had prayed, the place was shaken where they were assembled together; and they were all filled with the Holy Ghost, and they spake the word of God with boldness. (Acts 4:24,31)