While (I think) there is no argument over the Istari being originally Maiar - are they still Maiar? Did they cease being Maiar when they incarnated themselves?
Clarification: many official (e.g. UT) and unofficial (e.g. wiki) sources say that they were Maiar, but not that they are Maiar. Are Saruman, Gandalf and Radagast still Maiar even in the third age?
Yes, undoubtedly. You're misinterpreting the word "were." When Christopher Tolkien wrote "they [the Istari] were all Maiar" the use of past tense refers to the time during which the story occurs; it doesn't mean that they underwent a change of kind.
As far as we know change of kind isn't possible. It would certainly require the direct intervention of Eru. (As occurred when Aulë created the Dwarves.) Tolkien is quite clear that men cannot achieve immortality by setting foot in Aman. Half-Elves are allowed to choose "under which kindred they shall be judged." It's never said that they become a member of their chosen race. The closest would probably be Luthien, who gave up immortality to share Beren's fate (that is, death). The "shared fate" wording is important; Luthien died but she did not become human. There is also, perhaps, the question of orcs. Tolkien originally envisioned them as Elves that had been twisted and corrupted by Morgoth but moved away from that idea later. He never settled on their origin.
You must have gone to the Elves for advice, for the answer is both "no" and "yes".
No, they are not Maiar because they lack essential traits of the Maiar. In the Silmarillion, it says:
With the Valar came other spirits whose being also began before the World, of the same order as the Valar but of less degree. These are the Maiar, the people of the Valar, and their servants and helpers.
and
Now the Valar took to themselves shape and hue; and ... they took shape after that manner which they had beheld in the Vision of Iluvatar, save only in majesty and splendour. Moreover their shape comes of their knowledge of the visible World, rather than of the World itself; and they need it not, save only as we use raiment, and yet we may be naked and suffer no loss of our being.
Therefore with the Valar came other spirits whose being also began before the World, of the same order as the Valar but of less degree. These are the Maiar, the people of the Valar, and their servants and helpers.
This strongly suggests that the Maiar also could "walk unclad" and take to themselves "shape and hue". We also know that Sauron could do so and that he was a Maiar. Yet it seems pretty clear that neither Gandalf nor Sauruman could.
So they, therefore, were not Maiar at least while they were embodied in Middle-earth.
But also, "yes" they were still Maiar: We know so little of the nature of the Valar and Maiar that an equally consistant and reasonable answer is that they were Maiar who accepted, for a time, a diminution of their power, but were still Maiar. Is not a human who for a time wears a blindfold still human even though suffering a significant diminution of power?
Ultimately, the answer depends on details of the nature of the Maiar and the Istari that we simply don't know.
Yes, undoubtedly Tolkien implies they still were Maiar, even if there's no direct quote to prove they were. Consider:
We know Gandalf was physically capable of feats no human could accomplish.
From The Return of the King, Appendix B, "The Tale of Years" (All cited dates are Third Age):
3019
January 15 The Bridge of Khazad-dûm, and fall of Gandalf.
January 23 Gandalf pursues the Balrog to the peak of Zirak-zigil.
January 25 He casts down the Balrog, and passes away. His body lies on the peak.
Gandalf pursued and fought the Balrog for eleven days, inclusive of end points. He dies at the end, but doesn't die along the way. I shouldn't imagine he and the Balrog spent their lunchtimes at the Zirak-zigil Cafe, or napped in their cubicles. There's no indication of food, water, or rest. To answer the question, he keeps going without all that. We can conclude he feels the hunger, and thirst, and fatigue, but needing to relieve them doesn't enter in to it.
The fight clearly must have been Maia vs. Maia, hand to hand, uncloaked.
Based on these facts we can deduce that Gandalf's spirit, his ëalar, can, when pressed, fully take over his body, which is that of a Man, real and not feigned.
If that isn't an Ainu's capability vs. a Man's I don't know what is.
