The Cross has been a symbol used by Christians for the past 1,600 years or so. The moon's crescent has been a symbol used by Muslims, probably inherited from the Ottoman Empire in the 15th century.
There are many well-documented similarities between Islam and Christianity. However, the two religions also have significant differences. Ignoring for the moment, hybrid 'Chrislam' groups, there have also been gallant attempts by several people to engage in serious Islamic/Christian dialogue.
The differences between the two religions are NOT sufficiently strong for Muslims and Christians to fight one another. Indeed, they both consider war to be intrinsically wrong. We must look to other factors such as basic human greed, jealousy and an urge for power and supremacy, to see the real cause of so-called 'religious' wars.
Both Christianity and Islam have exclusive natures, although these have been watered down by modern thinking statements such as Vatican II. An increasing number of people are accepting the view that democracy is good and that part of this democracy is an acceptance of social equality and respect for other groups within society.
In the Crescent Cross image above, the cross is black and the crescent is green. Apart from green being the traditional Islamic colour, there is no real significance in the colours; they exist merely to delineate the two shapes.
The Crescent Cross is neither a cross adorned with a crescent, nor a crescent adorned with a cross. It is an interfaith symbol where both the crescent and the cross bear equal significance. It is an interfaith symbol, but not a religious tolerance symbol, since it excludes other symbols; notably the Jewish Magen David (Star of David). Indeed, by some people it is considered anti-Semitic.
See other Crescent Crosses
Generally with symbols, the moon is shown as a crescent and the sun is shown as a circle
See for example, the International Federation of Red Cross and Red Crescent Societies ICRC