Is it permissible to go paintball shooting?
It is important to point out that if this is regarding a camp activity, then whatever written further below has no bearing on what should be done in camp. The purpose of this answer is not for staff members – in contrast to the director – to take this answer and make a Balagan in camp with it. The camp has their Rav who they ask their Shailos to, and that is what is to be followed in the camp B’Poel Mamosh.
According to Halacha, one should not hit oneself nor shall he hit anyone else even if he gives permission, for it is not his body to give permission to hurt (and an Issur D’Oraysa might be involved).
Some Rabbonim permit paintball shooting as a school or camp activity to encourage learning and/or proper behavior (i.e. as a trip for for good learning) – similar to the concept of hitting a child to help his learning.
Others argue that it is only Assur to hurt someone if done in a harmful manner, however, since paintball shooting is done in a friendly manner there is no Issur involved. Nonetheless, this Heter should only be used if it is L’Toieles.
Indeed, tackle football is regularly played in many otherwise religious schools and camps. However, there is an obvious distinction since here there are guns used for shooting and hurting, while tackling is not officially to attack.
While these arguments might justify the Minhag to be lenient, there is strong room to adopt a stringent approach, as per the straightforward reading of Halacha (referenced below).
I would add that if we don’t steal the Afikoman, which is a Minhag because it involved stealing, even though it’s only a game, we definitely shouldn’t shoot other Yidden and hurt them, even as a game. It appears to be very against our Shito. As mentioned, camps must formulate a policy with their local Rav on this matter. It’s certainly against our Shita for staff members to decide on their own how to run the camp.
Rambam Hilchos Choivel U’Mazik Beginning Perek Hey. The Rambam uses the words Derech Nitzayon, in a fighting manner. See Alter Rebbe (Shmiras Haguf Se’if Daled). Igros Moshe Choshen Mishpat Chelek Aleph Siman Gimmel and Kovetz Ha’aoros (Wasserman) Yevamos Siman Ayin.
ולהעיר מדוגמתו, אף שיש לחלק קצת, בשלחן מנחם ח”ז סי’ לט (מלקוטי שיחות ח”כ עמ’ 568): “על דבר לעשות נקב באזנים בשביל נזם אוזן כו’, בטח העונג הממושך מקישוט הנ”ל גדול שלא בערך לגבי הצער דהגוף ברגע הנקיבה, ולכן מותר הוא אף 1) בגדולה; 2) שיש מתקשטות בהנ”ל מבלי עשיית נקב (כיון שאינו רגיל כל כך, ועוד ועיקר – שאז יש צער קצת בכל פעם פון קוועטשן האוזן)”.