Hello! Sorry if this is a bit of a late response.

In short - it really depends on the Manx person involved. There were plenty of families from the island that were demonstrably Manx in origin but achieved considerable success in the nascent British Empire. Earlier in the century we have the likes of men such as John Quilliam of Trafalgar fame, the young Mark Cubbon who would later become Governor of Mysore, and Colonel Mark Wilks who would end up as governor of St. Helena and - briefly - would befriend the exiled Napoleon. There is no solid evidence that these men experienced any particular discrimination for their origins as Manxmen, but we should take note that these men were Manxmen of a different social class and were basically a part of 'normal' upper-middle class society in Britain at the time, effectively English in manners and customs and would perhaps be best compared to the Anglo-Irish elite, arranging marriages with established genteel families in England. Their most 'Manx' attributes would be their family names and perhaps an appointment to a position as a Member of the House of Keys, as well as connections to properties and holdings on the island at the time, but these were English-speaking gentlemen.

Discrimination against the Gaelic-speaking 'lower' elements of society appears to be a little more prominent, but very much dependent on the perceptions and attitudes of the individual rather than broader trends. Most of this has yet to be explored in an academic sense, so most of the sources at hand are going to be purely primary. My recommendation would be to take a look at the guides to the island written around 1800 and get a sense of how perceptions varied; in some, such as Feltham's Tour of 1798, he describes the Manx as being:

"[...]of a swarthy complexion, stout, with an air of melancholy pervading their countenances; the men are indolent, but the women are active and lively[...]".

Yet some of these accounts viewed the Manx with a kind of condescending fondness; from a letter published in Walker's Hibernian Magazine of December 1802:

"Those who visit the Manks, will find them not very unlike their neighbours, and yet with characteristic traits sufficiently distinguishing. The men are, in general, tall, stout, and well-proportioned; boisterous yet kind; warm in their attachments; " sudden and quick in quarrel; possessing general information, but seldom profound erudition. The inferior order, obliged to slave with the utmost perseverance during the continuance of the fishing season, seem then to exhaust their activity, and for the remainder of the year sink into a state of the deepest torpor."

In terms of discrimination against Manx people when working or living beyond the island... the evidence simply isn't there to the best of my understanding, at least for those common people travelling or working abroad. This largely stems from the fact that most of the people that could face potential discrimination would be monoglot Manx speakers and those not accustomed to life outside of the Isle of Man. All these perceptions stem from accounts written about the Manx rather than by the Manx, which should be taken into account as all their behaviours, customs and so on are being viewed through the lens of genteel established British travellers, writers and clergymen. For the benefit of your writing, I would suggest taking a look at these accounts and have people in your story react differently depending on what they know about the island. A Manx gentleman or gentlewoman would probably not face much (or any) discrimination if their manners and social behaviour were very much fitting into the norm of society, but a lower-class Manx person who may be a monoglot Manx speaker could potentially face discrimination depending on who meets them. I do not get a sense though that this discrimination was because the Manx were ostensibly 'Celtic' or because some may have perceived a shared connection with Ireland, but rather more that the language and customs of the Manx were simply alien to many people and would be treated with suspicion. Again, there is very little solid evidence - especially so far from native lower-class Manx people, but I hope this has been of some use to you! As I said before, academic writing about this topic is very scarce and you will have to engage with primary sources to get a clearer picture for how your period piece might be constructed.