Muslims or Mohammedans?

The former is the established present usage. The latter is an old one deemed insulting as Muslims do not worship their prophet.

But why is it that they react more strongly to perceived disrespect for their prophet than their Allah? When we lived in Nigeria, Allah's name was constantly take in vain.

How much?
Ten Naira.
Allah?
Allah!
i.e Is it so? Yes it is.

They would not dream of substituting Moh's name.
Why is a mere man so revered?
I think it is because Allah is so transcendent, so remote and other that no personal relationship is possible. Th Sufis do try. But for most Muslims, obeying God is doing what Mohammed did. You look to the Hadith to find what is the tradition - which shoe to but on first, how to clean your teeth etc.

Christians have WWJD but what Jesus did is not necessarily normative. He came to die not to give a comprehensive template for living. So we’re not to ask, “What did Jesus do?” so we could copy what he did. But we’re to ask, “What has Jesus done?” because he has done all for our salvation. The gospel is Christ’s life, suffering, death, resurrection, ascension and session at God’s right hand. There’s nothing in that gospel that we could do.–

But for the Muslim, their prophet's life is the great template. Isult him and they are insulted too.

Of course it has its limits. I do not see Muslims riding to the mosque on a camel. It is a bit like those Christians who reckon they have a Regulative Principle of Worship. The early church had no buildings but they do.

But Muslims really are followers of Mohammed and may be so named I believe. I won't do it because I want to be friendly. I respect them, not their false prophet.