Na stadionie nie powinno się kłócić z innymi kibicami, nawet jeśli mecz jest ważny.

It is an impersonal way to say one should not or people should not.

So Nie powinno się kłócić... means something like:

• One shouldn’t argue...
• People shouldn’t argue...
• You shouldn’t argue... in a general sense

It is very common in Polish to use this kind of structure instead of naming a subject directly.

Because this is an impersonal construction.

In a normal sentence, powinien / powinna / powinno / powinni agrees with a specific subject:

• On powinien – he should
• Ona powinna – she should
• Oni powinni – they should

But in powinno się, there is no specific subject. The form powinno is used as part of a fixed impersonal pattern, roughly equivalent to it is advisable / one should.

So nie powinno się does not mean it should not in a literal English sense; it is just the Polish way of making the statement general.

Because Polish often leaves the subject out when the meaning is general.

In English, you might say:

• You shouldn’t argue with other fans...
• People shouldn’t argue with other fans...

In Polish, instead of using a general you, it is very natural to say:

• Nie powinno się kłócić...

This avoids naming a specific person and sounds more like a general rule or recommendation.

The dictionary form is indeed kłócić się = to argue / to quarrel.

In this sentence, the się has moved earlier:

• nie powinno się kłócić

This is very normal in Polish. Short clitic words like się often appear before the infinitive, especially after the finite verb.

So:

• kłócić się z kimś = to argue with someone
• nie powinno się kłócić z kimś = one shouldn’t argue with someone

The meaning is exactly the same.

Polish often uses na with certain public places, venues, and events, including stadion.

So:

• na stadionie = at the stadium / in the stadium

Even though English often uses in, Polish prefers na here.

Also, after na when talking about location, Polish uses the locative case, so:

• stadion → stadionie

It is the locative singular.

The base noun is:

• stadion – stadium

After na meaning location, it becomes:

• na stadionie – at the stadium

So the ending -ie shows the locative singular form.

Because the verb kłócić się takes z kimś = with someone, and after this z, Polish uses the instrumental case.

So:

• kibice = fans, supporters
• z kibicami = with fans

The adjective must match the noun in case, number, and gender:

• inni kibice = other fans
• z innymi kibicami = with other fans

So both words are in the instrumental plural.

Kibic means fan or supporter, especially in sports.

So:

• kibic – one fan
• kibice – fans
• kibicami – with fans

In this sentence, innymi kibicami means other fans / other supporters.

Nawet jeśli means even if.

So:

• nawet jeśli mecz jest ważny = even if the match is important

Yes, jeśli could often be replaced by jeżeli, which is slightly more formal or just a stylistic variant:

• nawet jeśli
• nawet jeżeli

Both are correct here.

Because mecz is a masculine singular noun, and the adjective ważny must agree with it.

So:

• mecz – match, game
• ważny – important

Together:

• mecz jest ważny – the match is important

If the noun were neuter, you would use ważne instead.

Because nawet jeśli mecz jest ważny is a subordinate clause.

In Polish, clauses introduced by words like jeśli are normally separated by a comma:

• ..., nawet jeśli mecz jest ważny.

This is standard Polish punctuation.

It is more like advice or a general rule, not the strongest possible prohibition.

• nie powinno się = one shouldn’t / people shouldn’t
• nie wolno = one must not / it is forbidden to
• nie można = one cannot / one may not

So Nie powinno się kłócić... sounds like this is not appropriate or this is not what people should do, rather than a strict ban.