Though I didn't link to it as I already had a link in the post. The fact that the BBC said Adams was stepping down from the House of Commons in order to stand for the Dáil made me wonder if that page you linked to simply omitted the rule about being a member of a foreign legislature as being either too esoteric to worry about or too obvious to need mentioning. (Then again, you wouldn't think it'd be too esoteric in a country like Ireland which has such strong links with a devolved part of another country.)

Do you know what the actual statute is that governs eligibility for the Dáil? I tried to find it but without success.