By saying it's a dogwhistle are you saying that not adding the correct diacritics is considered racist by Irish people? If I change the rest of the sentence to Na Gaeilge will that be better.

No, I'm saying that it's associated with a certain outdated and bigoted attitude toward the Irish.

Using Éire in English, would be seen as odd. You wouldn't say Deutschland or Danmark.

> If I change the rest of the sentence to Na Gaeilge will that be better.

No. And you've used the genitive instead of nominative there, so I have some doubts that you could.