Irritation due to breathing noises in dojo

Yes the buddha even claims that noise is thorn to set the citta into samadhi, like here http://www.leighb.com/an10_72.htm

As usual, irritations stem from clinging. this is why ajhan brahm says to rely on wisdom power in order to set the citta into samadhi, instead of will power. In other words, being kind to what is experienced, even the most toxic thoughts, and pushing away bad thoughts in order to avoid having a toxic mind, like here https://www.youtube.com/watch?v=7aHSE3H2OCs

This is because to set the citta into samadhi, mano must have piti and the body must be tranquil. like here from the famous sutta

For a person endowed with virtue, consummate in virtue, there is no need for an act of will, 'May freedom from remorse arise in me.' It is in the nature of things that freedom from remorse arises in a person endowed with virtue, consummate in virtue.

"For a person free from remorse, there is no need for an act of will, 'May joy arise in me.' It is in the nature of things that joy arises in a person free from remorse.

"For a joyful person, there is no need for an act of will, 'May rapture arise in me.' It is in the nature of things that rapture arises in a joyful person.

"For a rapturous person, there is no need for an act of will, 'May my body be serene.' It is in the nature of things that a rapturous person grows serene in body.

"For a person serene in body, there is no need for an act of will, 'May I experience pleasure.' It is in the nature of things that a person serene in body experiences pleasure.

"For a person experiencing pleasure, there is no need for an act of will, 'May my mind grow concentrated.' It is in the nature of things that the mind of a person experiencing pleasure grows concentrated.

THis is accomplished through sati sampajana. Indeed, becoming mindful means tracking and sorting the thoughts according to what the buddha claims are good thoughts and to destroy bad thoughts, same thing with vedanas and sannas, like here https://www.accesstoinsight.org/tipitaka/mn/mn.019.than.html

With mindfulness, meaning sati sampajana, the mano becomes so much full of sammasankappa [=avoiding desire and ill will], that the Nīvaranas [=5 hindrances] are contained, that piti arises and then the citta sits in samadhi, where the hindrances are suspended.

Of course the puthujjanas who despise Nekkhamma will never have sati, let alone set the citta into samadhi. THose people prefer to create a fairy tale where they see themselves as good people, even though all they do is stay addicted to sensuality, as explained,

"Whatever a monk keeps pursuing with his thinking & pondering, that becomes the inclination of his awareness. If a monk keeps pursuing thinking imbued with sensuality, abandoning thinking imbued with renunciation, his mind is bent by that thinking imbued with sensuality. If a monk keeps pursuing thinking imbued with ill will, abandoning thinking imbued with non-ill will, his mind is bent by that thinking imbued with ill will. If a monk keeps pursuing thinking imbued with harmfulness, abandoning thinking imbued with harmlessness, his mind is bent by that thinking imbued with harmfulness.

I hear other people breathing loudly through their noses, it drives me nuts and puts me in an extremely bad mood.

You are quite fortunate to have these kind souls gently show you the rough spots in your meditation. If you were alone, steeped in quiet, there would be no such disturbance. If there is suffering somewhere, it is attached to delight (MN1). For example, if one delights in quietness, seeking refuge from chaos on the cushion, then such disturbances would irritate. It would irritate especially if there is a sense of "my meditation" and "their noise". This is identity view and SN22.155 says:

But by not grasping what’s impermanent, suffering, and perishable, would identity view arise?” “No, sir.”

Breathing noises come and go. In and out. They are not permanent. Instead of thinking "that person keeps breathing loudly!", simply think "There is an in-breath." Later, notice that "There is an out-breath". In doing so, the impermanence manifests. Seeing the impermanence, the next step is to recognize that it really has nothing to do with you:

This is not mine, I am not this, this is not my self --MN62

Knowing that this is not your self, simply count your own breath and return to that peace you thought threatened. It's not just your peace, it's also their peace. They, over there, are hearing your own breathing. Give them the gift of peace by gently attending to your own breath.