The fornicator does not marry except a [female] fornicator or polytheist, and none marries her except a fornicator or a polytheist, and that has been made unlawful to the believers.
If my interpretation is correct, this clearly says if you commit adultery, you can only marry another Muslim adulterer, or a non Muslim. Is this interpretation correct? Am I missing something?
First, let us define some of the words that were translated, a mushrik is just someone who committed an unforgivable crime, it does not necessarily mean a polytheist, this is just one of the crimes that are considered shirk. Of the crimes that are considered shirk, adultery is one or them, so a mushrik can also refer to an adulterer.
The ayah says that they can marry an adulterer or a mushrik. This does not mean Allah gave permission to marry a non-beliver, it means they are only allowed to marry an adulterer, and it adds or a mushrik to point out that the two words are synonymous, it is not giving a second option to marry a non beliver.
The reason for this is because they person who committed adultery in not worth a believer who has not sinned, so they shouldn't marry. A Muslim should marry someone who is as good as them, and in Islam a persons worth is calculated by their sins and good deeds. An adulterer is no longer as good of a Muslim as the believer is hence, they cannot marry them.
From Holy Qur'an:
And do not marry Al-Mushrikât (idolatresses, etc.) till they believe (worship Allâh Alone). And indeed a slave woman who believes is better than a (free) Mushrikah (idolatress, etc.), even though she pleases you. And give not (your daughters) in marriage to Al-Mushrikûn till they believe (in Allâh Alone) and verily, a believing slave is better than a (free) Mushrik (idolater, etc.), even though he pleases you. Those (Al-Mushrikûn) invite you to the Fire, but Allâh invites (you) to Paradise and Forgiveness by His Leave, and makes His Ayât (proofs, evidences, verses, lessons, signs, revelations, etc.) clear to mankind that they may remember.
Surah: Al-Bakara, 221
This verses around is the answer to your question -
[24:2] "...And let a group of the believers witness their punishment."
[24:3] "...The fornicator does not marry except a [female] fornicator or polytheist,..."
If you have witnessed lashing of a fornicator, you should not let any believing person marry them. This is a part of the punishment of fornication in an Islamic state.
So if some one has been punished for fornication publicly (4 witnesses etc), its a part of their punishment that they would not get a believing person in marriage.
This is just like in the west, when you do an accident and apply for car insurance anywhere, you would end up being punished for that accident even if it was 25 years before the fact. Your record kind of gets ruined.
Just to put things in perspective, we also have verses like -
[2:221] "And do not marry polytheistic women until they believe...."
How would you know that they are believers? can someone look into their hearts and see if they have really started to believe ?,
Its about "public" declaration, just like above. If a person is publicly declared "fornicator" or "they are not believers" they don't get believing muslims for marriage
First of all Some expressions is not allowed to be linked together, we have to differentiate between marriage and adultery as crime. Muslim males are allowed to marry Muslim and non-Muslims females except where she is a polytheist. But non-Muslim males as general can't marry from Muslim females at all. Secondly the only crime that is considered to be unforgivable is polytheism, because Allah defined him self to be Alrahman Alrahim which means that Allah is the most clemency.
