We have references in Polybius, Histories, II-28 (emphasis added):
The Insubres and Boii wore their trousers and light cloaks, 8 but the Gaesatae had discarded these garments owing to their proud confidence in themselves, and stood naked, with nothing but their arms, in front of the whole army, thinking that thus they would be more efficient, as some of the ground was overgrown with bramblesb which would catch in their clothes and impede the use of their weapons.
In Diodorus Siculus, Library of History, V-30 (emphasis added):
The clothing they wear is striking — shirts which have been dyed and embroidered in varied colours, and breeches, which they call in their tongue bracae; and they wear striped coats, fastened by a buckle on the shoulder, heavy for winter wear and light for summer, in which are set checks, close together and of varied hues. For armour they use long shields, as high as a man, which are wrought in a manner peculiar to them, some of them even having the figures of animals embossed on them in bronze, and these are skilfully worked with an eye not only to beauty but also to protection. On their heads they put bronze helmets which have large embossed figures standing out from them and give an appearance of great size to those who wear them; for in some cases horns are attached to the helmet so as to form a single piece, in other cases images of the fore-parts of birds or four-footed animals. [...] Some of them have iron cuirasses, chain-wrought, but others are satisfied with the armour which Nature has given them and go into battle naked.
It seems to have been mainly poorer celts on certain occasions and places who fought naked. Not their leaders or the better off. We know that celts often wore armour. So simply saying the celts fought naked is a gross over simplification. Some celts did in specific locations and specific circumstances.