Mindegy, melyik csészét hozod, csak tiszta legyen.

Mindegy is a very common Hungarian word meaning it doesn’t matter or it’s all the same.

In this sentence, it sets up the idea that the choice of cup is not important:

• Mindegy, melyik csészét hozod = It doesn’t matter which cup you bring

It often works almost like a complete sentence by itself:

• Mindegy. = Whatever / It doesn’t matter.

So here it introduces the whole first idea: the speaker is saying the specific cup is irrelevant.

Because Hungarian often lets mindegy carry the whichever / no matter which meaning.

So:

• melyik by itself means which
• but Mindegy, melyik... naturally means It doesn’t matter which...

In other words, Hungarian does not need a special word equivalent to English whichever here, because that sense is already created by mindegy.

Because csészét is the accusative form, and it is the direct object of hozod.

• csésze = cup
• csészét = cup as the thing being brought

So:

• hozod a csészét = you bring the cup
• melyik csészét hozod = which cup you bring

The ending -t marks the direct object. In this word, the final vowel also changes length:

• csésze → csészét

That kind of vowel lengthening is normal in many Hungarian nouns.

Because Hungarian uses the definite conjugation here.

• hozol = you bring with an indefinite object or no object
• hozod = you bring it / you bring the specific one with a definite object

Even though English says which cup, Hungarian treats melyik csészét as a specific choice from a known set, so the verb is definite:

• Melyik csészét hozod? = Which cup are you bringing?

Compare:

• Milyen csészét hozol? = What kind of cup are you bringing?
  Here the object is not specific, so hozol is used.

This definite vs. indefinite verb distinction is one of the big grammar points in Hungarian.

Because Hungarian usually leaves subject pronouns out when they are clear from the verb ending.

• hozod already tells you the subject is you singular

So Hungarian normally says:

• hozod = you bring it

rather than explicitly adding te.

You could say te hozod if you wanted emphasis, but in a neutral sentence it is unnecessary.

Because the subject is understood from context.

The implied subject of legyen is the cup:

• csak tiszta legyen = just let it be clean / as long as it is clean

Hungarian often omits things that are obvious. Since the cup was just mentioned, there is no need to repeat it.

If you wanted to make it explicit, you could say something like:

• csak a csésze tiszta legyen

but that is less natural in this context because the subject is already clear.

Legyen is the 3rd person singular imperative/subjunctive form of lenni (to be).

Here it does not mean a command in the simple English sense. It is being used to express a requirement or condition:

• csak tiszta legyen = it just has to be clean
• or more naturally: as long as it’s clean

Hungarian uses this form very often after ideas like:

• wishes
• conditions
• requirements
• what matters or does not matter

So legyen fits the meaning the only requirement is that it be clean.

Because tiszta is an adjective, and here it describes what the cup is.

• tiszta = clean
• tisztán = cleanly, or sometimes clearly

With lenni (to be), Hungarian normally uses the adjective:

• A csésze tiszta. = The cup is clean.

So in this sentence:

• csak tiszta legyen = just let it be clean

Using tisztán would be wrong here, because that would be an adverb, not a description of the cup itself.

Literally, csak often means only or just. But in this sentence it has a slightly broader function.

Here it means something like:

• just
• the only thing is
• as long as

So:

• csak tiszta legyen

means that cleanliness is the one thing that matters.

A natural English rendering is:

• as long as it’s clean
• just make sure it’s clean

So yes, the core meaning is still only/just, but the full effect in context is stronger than a simple word-for-word translation.

Not completely. Hungarian word order is flexible, and different orders can shift the emphasis slightly.

The version in your sentence:

• csak tiszta legyen

highlights tiszta nicely, as the important condition.

You may also hear:

• csak legyen tiszta

This is also natural, but it sounds a little different in rhythm and emphasis.

So the original sentence is perfectly normal, and its word order helps underline the point:

• the cup itself does not matter
• its cleanliness does

Yes, that is possible.

Hungarian often allows hogy before a subordinate clause, and you may hear both:

• Mindegy, melyik csészét hozod
• Mindegy, hogy melyik csészét hozod

The version without hogy is very natural and compact, especially with question words like melyik, ki, mit, hol, and so on.

So in this sentence, the shorter version sounds very good and idiomatic.