Living with Mohammed or contemporary to the rise of Islam generally?

The sources from 7th century Hedjaz aren't good enough for anyone to reliably state the contemporary Muslim views of Mohammed, never mind non-Muslim.

The historiography of hadith is an absolute black hole, as it's oral history written down long after the fact. It's a hugely controversial subject, and the fact remains that's there is very little that an academic historian can say about the life of Mohammed with any degree of accuracy without at least acknowledging the huge problems of relying on the hadith or even the Quran.

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If you want contemporary sources relating to non-Muslims views of Islam in the time period generally, the most comprehensive work is "Islam as Others Saw It" by Robert Hoyland.

The best answer to your question is that it varied:

"While some saw Muslims as a punishment sent by God for their collective sins or the sins of the emperor, Jews saw Muslims as an instrument of God's deliverance. Muslims were also seen as primitive monotheists. However, the view of Islam as worldly that occurs in martyrologies written by ascetics should be related to the larger issue of asceticism, which was given new meaning by the worldly success of Islam and was also an issue among early Muslims. Although the non-veneration of images and worship toward the south appear to be new issues, Hoyland's point that Christians recycled old arguments against Judaism and used them against Islam should be extended to include Zoroastrians, who recycled old arguments against monotheism." From a book review by Michael Morony.

Edit: removed a line of speculation on my part.