I've done some study into the English and Dutch perception of the Irish during the seventeenth century. The evidence is clear that in those areas at that time, stereotypes did exist.

The English view of the Irish was very much a negative one in the Early Modern Period. David Hayton has described it as ‘wild and uncivilised, even uncivilisable, regressive in his way of life, pagan in his religion, licentious in his sexual mores, treacherous and savagely violent: in short, a dangerous barbarian’ (Hayton, Ireland after the Glorious Revolution, 1692-1715 (Belfast, 1976), p3).

However, this view altered in the second half of the seventeenth century. Around 1650, the Irishman was still seen as a blood thirsty barbarian, but by 1700, he had mostly become a comical figure, an ‘ignorant Teague'. The term ‘Irishism’ had come to mean an ‘inversion of logic or blundering with words’. (See J.G. Simms, Jacobite Ireland, (Dublin, 1969), p. 84-9). The change was most likely the result of Jacobite defeats in the Williamite War (1689-91). With the Irish no longer a realistic threat, a patronising attitude took over.

On the other hand, the Dutch, over most of the seventeenth century, had no opinion of the Irish at all. Ireland was at the margins of Europe, and the then mighty Dutch simply had no interest in the country.

When Ireland temporarily became pivotal in European and Dutch history (in the above mentioned Williamite War), there was a brief surge in interest in the country. Unlike the English, the Dutch never saw the Irish as a threat, as, while Ireland temporarily became a main theatre of war, its people were in reality rather inconsequential to the whole affair. As a result, Dutch opinions on the Irish were not especially negative. One pamphleteer describes them:

‘The [Irish], in general, are of stout stature, and very quick and nimble, big and strong in spirits, clever, war-minded, and asking little from their lives. [They are] tolerant of cold, work and discomforts, [...] benevolent to strangers, single-minded in love, but uncompromising in hate. [They are] gullible, desire fame and are impatient with contempt. They are somewhat too disposed to idleness, considering it a great wealth if they do not have to work but [can instead] have their freedom to do whatever they want. Then added are superstitions and false beliefs, going so far that they even honour the moon; as soon as they see the new moon, the farmers commonly kneel, and speak a Pater Noster, after us as healthy as you find us.’ (L. van den Bosch, Yerlant verlost en hersteld door de onvermoeide victorieuzen William de IIIde, koning van Groot-Britannien (Amsterdam,1690) (Knuttel catalogue, no 13397)).

In England after the Glorious Revolution (1688), there was a very strong negative reaction against the large numbers Dutch that came into the country; a PhD dissertation was written on the topic by Gregorius van Alphen (De stemming van de Engelschen tegen de hollanders in Engeland : tijdens de regeering van den koning-stadhouder Willem III, 1688-1702 (Assen, 1938)) which is an excellent read (if you happen to read Dutch!).

I have found, in the Dutch archives, similar references to stereotypes about the French, who were the Dutch Republic's main enemies in the late seventeenth century, as well references to supposed English and German characteristics. There may have been others again which I didn't specifically note.

This, I think, strongly suggest that in the seventeenth century at least, national stereotypes did exist. This does not prove when they started to occur; hopefully someone else will contribute about an earlier period.

It also means that by then, in answer to the second part of your question, at least in the case of England and the Dutch Republic, the two geographic areas my studies in this area have been confined, such stereotypes were quite popular in nature. They were communicated in pamphlets which were quite widely read and shared. In England, the fear of the Irish led to small scale popular risings in some places.

I suspect they were always common, and generally motivated by fear and misunderstanding, especially in the context of wars etc. In the period I studied governments and monarch deliberately tried to manipulate public opinion on others (the enemy!) by using propaganda. The printing press played a key role, though the oral spread of information was still important too.