"In our country, if one refers to Allah or mentions kalimah Allah, it will bring to one's mind that it refers to the god for Muslims. Kalimah Allah is sacred to the Muslims and put at the highest position, and its sanctity must be protected," he said Monday, according to local sources
The above quote is taken from here. Regardless of the use of Allah, what's clear in this article is that Muslims too recognize they refer to and worship a DIFFERENT God than Christians.
If Christians and Muslims both acknowledge that the God Christians worship is different from the object of Muslim worship, why do people go around suggesting: "We all worship the same God"? That fact is ... we don't! Any statements to the contrary reveal either naivete or ignorance, or arrogance in suggesting the holder (without authority) knows more than all the adherents to the other religions.
Note also the statement in the article:
The use of the word ‘Allah’ by other religions may arouse sensitivity ... among Muslims," explained Abdullah Zin, the de-facto minister for Islamic affairs,
While the suggestion that such use "may arouse sensitivity" may refer to cultural considerations or may even underlyingly serve as a threat, what's clear is that Muslims would not take lightly the suggestions of those that would suggest their object of worship is no different and should be mingled or interchanged with others.
While Christians who worship in spirit and in truth recognize it's a sin to take God's name in vain, we also recognize the authority and power given to the church today is spiritual and ecclesiastical (as opposed to physical or civil) and as such we neither possess the power of the sword physically nor are we to assume that power for ourselves individually for to do so would be to usurp the authority of the Scripture and to strike or kill people (apart from legitimate authority acting in accord with God's Word) would be to commit sin.