I've been doing a fair bit of thinking on this issue in figuring out which songs I should work to learn and which just aren't for me. Along with others above, there are many traditional songs I'm quite comfortable singing,though they are obviously from a male perspective: (Red is the Rose, Palace Grand, Lass of Glenshee, Adieu Sweet Lovely Nancy) .

There are other songs I'd LOVE to sing, but in my own head they're just TOO much in need of a male voice & presentation. For a Bob Dylan theme song circle, I would dearly like to bring Eric Bogle's brilliant song about singing like Dylan, but I don't have Leadfingers' panache in being able to tweak the humor of a genderbending presentation. In a recent bawdy songs workshop, I found I could NOT bring myself to sing one verse of a song that made reference to actions with a body part I don't have. Other verses where I'm singing first person as a rowdy young man, I had no problem with... and I can't say exactly WHY I drew the line particularly THERE, but I certainly FELT it.

I give a loud HUZZAH!! to Kathy's comment:"I believe there are some songs that typically sound better when sung by a baritone-- ideally a large bearded one" - I too love those sea chaneys, but in the main, I'm more comfortable singing along with them (and the charming bearded baritones) than trying to lead 'em myself. But part of this is something besides gender - I'm not a sailor, haven't worked on a tall ship, closest I've come is windsurfing decades ago. This gets to the OP's idea of SHOULD a song be sung by... The issue in regard to larger concerns than gender has been addressed in other threads, I think, but it goes to the same issue of how you decide if a song is something you can sing with some authenticity.

There's a slew of Scottish songs I adore singing, but I only do it alone, since I don't have and can't fake a Scottish brogue. If they're "Anglished" up, I do fine. When the rhyme scheme is dependent on dialect, I just have to be content to listen to someone with the accent sing it.

Since the OP was asking about "traditional Irish" songs, it might be rewarding to research songs you fancy and see which traditional singers have them in their repertoire. I'd guess there aren't so many songs that people feel STRONGLY that should be ONLY sung by one gender. It's your comfort level in what you sing, in the end, that dictates how you arrive at where you draw the Sing/Don't Sing line.

Joanne in Cleveland, a large, unbearded soprano