We have essentially three references on this topic. Of these, only Caesar's could have had political motivations, as he was engaged in a campaign against the Britons. His account, however, is only marginal compared to the others, in that he does not clearly state that the Celts went to battle naked. On the other hand, both Polybius and Diodourus Siculus look like reliable sources; they were Greek, not Romans. It is clear from their account that going in battle naked was uncommon between the Celts (see, in particular, the italicized part in the following passages).
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.
And finally in Caesar's de Bello Gallico, IV, 1, we learn that the Britons:
even in the coldest parts they wear no clothing whatever except skins, by reason of the scantiness of which, a great portion of their body is bare, and besides they bathe in open rivers.
There is plenty of archeological evidence for Celtic armor, especially helmets. Contemporary art (Dying Gaul, Ludovisi Gaul and Kneeling Gaul) has them always naked, but this is most likely due to either stylistic reasons, or because of the impression that accounts of naked warriors would have made on the artist.