1/ it is permitted, there are no rubrics against it.
2/ percussive instruments are generally not suitable, or are culturally associated with unsuitable musical styles. But 'the guitar' is a host of different things and different styles.
Beware swarms of hornets invading from neighbouring threads on this forum. I think if you have a budding Segovia you might try guitar.
3/ Pop or folk style playing is not suitable with any instrument, IMHO. (for the Stations)

Charles,

It is called the Ordinary Form, not the standard rite. I can not speak for you, but I do not merely absent the organ from Mass because GIRM tells me to do so.

Charles has dealt a coup de grace to this question.
Yes, Stations not being liturgy, one may use 'whatever instruments your pastor will allow'.
A sensitive judgment with respect to the 'spirit of the season', though, may and should temper one's choices.
Use 'what your pastor will allow', but choose to stay within a reasonably, recognisably Lenten ethos.
Taste is always one's most reliable tutor.

Usually at our parishes there is a mini parade inside church around the stations of the cross with guitarists sometimes.

I know taste is at stake here for many, but my main concern is actively involving our youth in the life of the church, not creating a perfect musical atmosphere.

The church is not about creating a perfect musical atmosphere, but preserving a prayerful tradition of music. A huge part of this is not using instruments that are commonly heard in popular music.

By encouraging this you are setting up a saxophonist to be turned away from the church when they move to another parish. I know this is not your goal.

Let them not sing - sad because they read music and could enhance the singing because of their abilities. Encourage them to hum. Seriously. Youth don't want things dumbed down for them.

Catholic high school students with an active music program at Mass have been known to refuse any of this music at Baccalaureate Mass - insisting on doing the music they do on Sundays and definitely not the school music. They are adults and want to be seen as such.

This is really irksome. (Tiresome, too!)
It is not the first time that someone has tossed, rather cavalierly, the incidence of the organ's appropriation as an entertainment medium at skating rinks and baseball stadia into our conversations - as if to insinuate that this noble instrument is, actually, ignoble. They might, as well, have tossed in its utter degradation by being adapted as so-called theatre organs by people who have more stupidly anti-creative instincts than brains, sense, or taste - not to mention zero respect for all that is noble in the human species. In such milieux the organ has been gussied up like a prostitute and used for base pleasures.

The truth is that no other instrument in history has such an existential relationship with Christ, his Church, his people, and his worship as does the organ. None. I'm sure that none here need a rehearsal of the organ's origins at the hands of a Greek engineer in Alexandria in the IIIrd century BC, its vicissitudes at the very top and the very bottom of Roman society - which is to say, as a treasured and highly august attribute of ceremonial surrounding the emperor, and, at the other end, its use in military ceremonial, and its likely very raucous use at the circus. After languishing forgotten in the embattled west, it remained an essential ornament of imperial ceremonial at the Byzantine court, from whence it traveled back to the west as a gift to the the court of Charlemagne, from whence it evolved as a distinctive attribute of liturgical embellishment on 'solemnities', and, finally, every Sunday in major churches and religious houses throughout the west. Its association with royalty and imperial ceremonial were, no doubt, factors in its adoption into the festal adoration of the divine Christ. (Nor is this the only borrowing from imperial ceremonial into Christian worship of the All Holy.) Further, the organ's speech by means of wind, its sustained tone, and the likeness of that tone to the human voice, as well as it being, thus, ideal for sustaining pitch and accompanying singing, could not have been lost on our mediaeval brethren. No other instrument has been or is so owned by Christ's flock, for over a thousand years now, enjoying a unique and profoundly existential relationship with his Church. The organ, dubbed the 'King of Instruments' by Beethoven, is the instrument of the King of kings. And, the Church has spoken: the organ, and only the organ, has been singled out by the Second Vatican Council as most suited for Christian worship. No other instrument gets so much as mentioned. None! (None!)

One can only wonder where those have been, on what planet they were born, who think of the organ only as it has been prostituted by the dregs of human intelligence.

(As an analogy on this topic, it occurs to me that, as everyone knows, the holy grail, the ultimate goal, of the alchemist was to turn lead into gold. Many were they, from early classical times throughout the mediaeval era, who devoted their lives to this hopeless end. On the other hand, we seem, now and then, here and there, to be plagued with those who take a perverse pleasure in attempting just the opposite, figuratively speaking, with respect to certain attributes of our 'goodly heritage': namely, that of turning gold into lead.)

could you even hear a violin over a saxophone?

Examples of how it actually sounds to us PIPs are rarely posted. These days it is easy to record on a mobile phone from the middle of the congregation. I think it would be illuminating, though care is needed to behave with due decorum.
This sort of thing is helpful even though not in the midst of the congregation.

o jeesh... now I am seeing Jesus carrying a guitar!

Get them to sing for the stations!!! Every muso needs to know how to and this could be your great opportunity for them to learn and pray.
Alternatively pick a feast and let them form a band and hold a party in the parish hall which can include some hymns but at least it isn't a liturgical setting. Liturgy isn't really my favourite place for those instruments. That could be great fun.

Utterly fascinating, how wickedly twisted such threads as this become, as Jackson intimated (tedious.) The OP wanted advice, not treatises.
Discretion is (always) the better part of valor.
PS. What the faithful thrive upon, vis a vis corporate song, is accuracy and stability. I know of many chanting celebrants/warbling "cantors" who are incapable of maintaining pitch and key accuracy, even within a simple chant/hymn/collect.
If you have a pilot voice who maintains intonation through "Stabat Mater" or whathaveyou, what need is there of instrumental accompaniment, unless it flawlessly and elegantly couches the melody and singing? Otherwise, it will decline to distraction.

Interesting, Mr Codova -
Perhaps something happened to the sackbut on the way to becoming a trombone?

quite good at making up their own laws and making their preferences into law

Not only the Prots. I know of an Order which claims to "have its customs"--but they are not licit. That Order has lots of churches in the US, all run by "canons."

@TheresaW what did you decide?

I never had to make this decision, actually, as those kids were unavailable. I think, if done tastefully, we could have used these instruments as accompaniment. But alas, I have no proof to either degree.