Salam (Peace) Samuel,
Thank you very much for contacting About Islam with your question.
In fact, the word “Allah” is only the Name of God in Arabic. Christians of the Middle East use the name “Allah” for God because they speak Arabic. Even if you look in the Bible in Arabic you will find the name “Allah” written where it says “God” in English.
There is no reason why Muslims should object to “Allah bless America”, as it means the same as “God bless America”.
Normally Muslims in public talks, or while in conversation with Non-Muslims, may use the word, “God” rather than “Allah”, to avoid using an Arabic word that people are not familiar with.
You can have as many slogans of this kind put up as you like, if this will help: Not only “Allah bless America”, but also, “Jehovah bless America”, “Bhagwan bless America”, “Ishwar bless America”, etc.
But as long as all these names stand for the one and only God, different names used by different peoples of different languages or religions I feel makes no difference.
Thank you. Please keep in touch and Allah bless you!
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