I'm responding to the OP without reading the thread. My wife has some Muslim relatives, and we've had live-in maids in Indonesia at times. So this is an issue I've faced.
Something to keep in mind is that the evidence seems to be that 'Allah' was a word used by Christians before Muhammad was born in the Arabic speaking world. They still use it. The Al Koran uses the word 'Allah' so a lot of Muslims won't translate the word since they consider it to be the name of the deity. There was a book about 20 years ago that argued that the Sabean pagans called the moon god 'Allah.' Maybe they did. But the Ugarits took the word 'El that would later be used in the Bible, and used it for the head of their pantheon who did things that did not resemble the true God.
The question arises as to whether they worship the same God. They claim to be worshippng the God of Abraham. Think about the Samaritans. If Josephus is right, one of the Samaritan kings named Sanballat hired the high priest's brother, who had kicked him out of the temple service for violating the Biblical priestly regulations by marrying Sanballat's daughter instead of an Israelite virgin or priestly widow. That priest set up a temple in Samaria. They had the first six books of the Bible, modified to make Mt. Gerizim the place of the true temple.
Jesus said 'ye worship ye know not what.' Maybe He was saying they didn't know what they bowed down to. The bowed down in prostration (worshipped) in the wrong direction. But they might have been confused about God, too.
As far as the Islamic concept of God goes, it is not the same as the Christian concept in a lot of ways. On the one hand, they affirm some of the Biblical characters who worshipped God, but they have some of their own mythologies about them. Their writings claim that Allah is the greatest deceiver of all, but Jesus said that Satan is the father of lies. The Al Koran encourages people to verify if it is true by looking at the Torah and/or the gospel. But Islamic teaching contradicts both.
For me, personally, I would definitely not want a Hindu idol in my home, or anyone bowing to idols. I wouldn't try to stop Muslim guests or employees from praying in their room away from other people. They don't set up a statue to bow to it. Honestly, I'd be more concerned with someone setting up a statue of Mary in my home and praying to it. They are trying to pray to the God of Abraham, but they don't have a Biblical concept of God. Plenty of secular Americans who had some exposure to Christianity occasionally pray without having a Biblical concept of God, either. At least they are trying to be closer to God, trying to do what they think God requires, even if they aren't reconciled to God and have a wrong 'concept of God'.
In Indonesia, Christians call God 'Allah' to. It's in the main Bible translation.