Thyme pronounced without the 'th' is not peculiar to Hiberno-English. I was taught, rightly or wrongly, that "thyme" and "Thames" were exceptions and that the 'th' should not be vocalised.

Most educated people in Ireland do pronounce 'th' in ordinary speech. Our ex-Taoiseach (prime minister) Bertie Ahern was an exception and people made fun of his 'dises ' and 'dats'.