If I grew up in a predominantly Muslim country, but was not a Muslim myself, would I have a problem if the money had "In Mohammed We Trust" on it? Probably not.
1) I grew up with money having that inscription, so it wouldn't be foreign at all to me, even though I don't subscribe to that faith. I don't usually look at money that closely and would probably forget what was on it, as I do now.
2) If I weren't forced or pressured to adopt the Islamic faith and were free to choose to believe or not as I wished, the fact that I am surrounded by adherents to that faith and their practices would not threaten me -- to each their own.
3) If, as in U.S., the laws of that country were not too closely tied to religious teachings, I would abide by the laws there as I do here (note that there are many things in U.S. that are unethical to do -- not what a Christian should do -- but yet are still legal).
4) Despite exceptions to the contrary, the teachings of most major religions support mostly positive behaviors that are good for societies and good for individuals. Honesty, loyalty, sincerity, industry, self-sacrifice, compassion for and service to others. What is not to like, whether it be my particular faith or that of another?
Not only wouldn't I have a problem in that situation, I wouldn't try to denigrate and deny the predominant faith in this hypothetical country, unlike some in U.S. who have imposed their will on our Christian majority. I call what they do "intolerance".