I recently saw this picture of Ismail I, and if there was no turban, I would think it was a typical portrait of a European ruler. This medal of Mehmet II also looks very positive, in that they both seem to portray Muslim rulers as if they were a normal European ruler, and not "the enemy."
Is this normal? Are there more examples of Sultans/Caliphs (or people that weren't contemporaneous rulers) portrayed like this? Also, I'm using the word positive, because I'd expect "demon burning in hell" to be the standard that all Muslims were at.
Also, I assume that this would have gone in the reverse too, right?
Your examples fall a few centuries out of my area of expertise, but no, these types of portrayals were not uncommon in the late 15th century and especially the 16th century for Ottoman sultans. There were important trade relationships to maintain between western Europe (especially Italy) and the Ottoman empire, and so we see these strangely elaborate and flattering portraits of notable Ottoman sultans and sultanas (the fashion of sultanas dresses and textiles were also imported to Italy). I know that Saladin (12th century) was treated to a similar style of portrait in the Renaissance, and he is the only pre-Ottoman Muslim I can think of off the top of my head who was treated with a great deal of respect by western rulers both during his lifetime and after his death. There may be more, but he is the one who springs to mind.
Veronese, Gentile Bellini, Titian (and his workshop) and other well-known Italians painted portraits of Ottomans-- the Uffizi has a terrific collection of these and I was trying to find the link for you to browse through them (they are not on display), but they've changed the search interface and I'm having trouble accessing the image base. There has been, in recent years, some interesting scholarship about these portraits and especially about the symbolism of the turbans (apparently, size DOES matter). I can try to find some references for you. Hope this helps a little-- I've always liked this portrait style, I've just never had the time to do much research on it or the politico/economic nuances concerning their production.
The medieval chivalry romances would often include a Saracen character who embodied the chivalric virtues despite being Muslim. Sir Palomides of Arthurian lore is probably the most famous, but there is also Feirefiz from Parzival by Wolfram von Eschenbach. However, both of those characters become Christian over the course of the story.