Both imams at-Tabari and ibn Kathir mentioned in their tafsir the following hadith:
In the Pre-lslamic Period when the people assumed Ihram, they would enter their houses from the back. So Allah revealed:-- "And it is not righteousness that you enter houses from the back, but the righteous man is he who fears Allah, obeys His Orders and keeps away from what He has forbidden. So enter houses through their doors." (2.189)
Imam at-Tabari mentioned further similar narrations on the authority of several other sahabah and tabi'yn (Also see in Tafsir at-Tabari here in Arabic).
Imam al-Bukhari in his Sahih and at-Tabari in his tafsir further mentioned:
I heard Al-Bara' saying, "The above Verse was revealed regarding us, for the Ansar on returning from Hajj never entered their houses through the proper doors but from behind. One of the Ansar came and entered through the door and he was taunted for it. Therefore, the following was revealed: -- "It is not righteousness That you enter the houses from the back, But the righteous man is He who fears Allah, Obeys His order and keeps away from What He has forbidden So, enter houses through the proper doors." (2.189)
These are the strongest statements on the topic and they can be summarized as follows -as done by at-Tabari-:
In the Jahiliyah, some people would avoid entering their house from the door if they were wearing Ihram.
He also summarized the interpretation of the full verse as follows:
In the following I'll translate from Arabic language, as these translations are of my own take them carefully!
قال أبو جعفر: فتأويل الآية إذًا: وليس البر أيها الناس بأن تأتوا البيوت في حال إحرامكم من ظهورها، ولكن البر من اتقى الله فخافه وتجنب محارمه، وأطاعه بأداء فرائضه التي أمره بها، فأما إتيانُ البيوت من ظهورها فلا برَّ لله فيه، فأتوها من حيثُ شئتُم من أبوابها وغير أبوابها، ما لم تعتقدوا تحريم إتيانها من أبوابها في حال من الأحوال، فإن ذلك غيرُ جائزٍ لكم اعتقادُه، لأنه مما لم أحرمه عليكم.
Abu Ja'afar said: So, the interpretation of the verse then: It is not righteousness, O people, that you come to homes when you are in ihram from their back, but righteousness is he who fears Allah, and is afraid of Him (His punishment), avoids His prohibitions, and obeys Him by performing the obligations that He commanded him to do.
As for coming to houses from their backs, there is no righteousness for Allah in it, so go to them from where you want from their doors and other than their doors, unless you think that it is forbidden to come to them from their doors in any case (or state), because that is not permissible for you to believe, because it is something that I did not forbid you.
Ibn abi Hatim counted five (slightly) different explanations with corresponding narrations and sources. One could summarize them saying:
That this verse means to say that the most important in Islam is taqwa (the fear of Allah), while what ever practices people may have practiced in Jahiliya (for example not entering houses from the (front) door, because one returns wearing ihram, or goes out or comes from a trip or journey or practicing I'itikaf are rather appearances which are not important as stated in the hadith:
" Verily Allah does not look to your bodies nor to your faces but He looks to your hearts," and he pointed towards the heart with his fingers.