He had anal intercourse with a foreign woman but they have repented. Is it permissible for them to get married?

Praise be to Allah.

Firstly: 

You should understand that looking for the right opinion on practical fiqhi matters is something good, and it indicates that a person is seeking the truth that Allaah has enjoined. Even better than this is that a Muslim should look for the correct belief that will save him from the misguided sects which the Prophet (peace and blessings of Allaah be upon him) spoke of. He said that there would be seventy-two sects, “all of which will be in the Fire” meaning that they are misguided and deserve this warning of Hell. 

If you both regret what you did and have repented sincerely, then it is permissible for you to get married, and there is no reason why you should not do so. 

As for what you say about ‘Umar ibn al-Khattaab preventing the one who married a woman during her ‘iddah from ever marrying her, it seems – if this is a sound report – that this was a punishment (ta’zeer) to the one who committed a sin, and it was not a confirmation of a shar’i ruling that this is haraam. 

What you have quoted from some of the Sahaabah, that they ruled that a couple who committed zina and then get married would remain adulterers forever, may be understood as applying to those who did not repent. 

Ibn Hazm (may Allaah have mercy on him) said: 

It was narrated from Ibn Mas’ood that he said concerning the one who marries a woman after committing zina with her: They are still adulterers. Then he narrated that Saalim ibn ‘Abd-Allaah ibn ‘Umar was asked about a man who committed zina with a woman then married her. He said: Ibn Mas’ood was asked about that and he said: “And He it is Who accepts repentance from His slaves” [al-Shoora 42:25]. 

Ibn Hazm said:  

The two opinions (of Ibn Mas’ood) are in harmony, because he only allowed marrying that woman after repentance. End quote. 

Al-Muhalla (9/63) 

And Allaah knows best.