You pray two Rak'ah to greet the masjid even during the Friday sermon
Jabir bin 'Abdullah reported:
Sulaik Ghatafani came on Friday when the Messenger of Allah (sallallaahu alayhi wa sallam) was delivering the sermon. He (Sulaik) sat down. He (the Holy Prophet) said to him: 0 Sulaik I stand and observe two rak'ahs and make them short, and then said: When any one of you comes on Friday, while the Imam delivers the sermon, he should observe two rak'ahs and should make them short.
[Sahih Muslim]
This hadith is not specific to any one individual as some people try to reinterpret it to defend the position of their Madhhab.
The correct opinion is that you will pray the two Rak'ah of greeting the masjid even if the kahtiib is in the middle of the sermon.
This is what the Messenger of Allaah (sallallaahu alayhi wa sallam) ordered. This is what you will follow. This is what any Muslim would follow.
The hadith does not contradict the hadith that you are supposed to stay silent during the sermon. There is no contradiction. Praying the two Rak'ah for greeting the masjid is excepted from the 'ahadith which tell you to remain quiet and attentive.
Some have claimed that it is possible that the above hadith is abrogated. This view has been put forth by the Maaliki school of thought. They say an abrogation is possible based on the following hadith:
Abu al-Zahiriyyah said:
We were in the company of 'Abd Allah bin Busr, the Companion of the Prophet (sallallaahu alayhi wa sallam), on a Friday. A man came and stepped over the people. 'Abd Allah bin Busr said: A man came and stepped over the people while the Prophet (sallallaahu alayhi wa sallam) was giving the sermon on Friday. The Prophet (sallallaahu alayhi wa sallam) said: Sit down, you have annoyed (the people).
[Sunan Abi Dawud]
They say the man was ordered to sit down. He was not ordered to pray the two Rak'ah. Hence, an abrogation is possible.
An abrogation cannot be assumed on a mere possibility. You need hard evidence for it. What we have in this instance is concrete evidence that the Messenger of Allaah (sallallaahu alayhi wa sallam) said:
"When any one of you comes on Friday, while the Imam delivers the sermon, he should observe two rak'ahs and should make them short"
[Sahih Muslim]
The Messenger of Allaah (sallallaahu alayhi wa sallam) gave the order to remain silent during the sermon.
He (sallallaahu alayhi wa sallam) gave the order to remain attentive.
And it is he (sallallaahu alayhi wa sallam) who said to the man who came and sat down to get up and pray the two Rak'ah to greet the masjid.
You follow the Messenger of Allaah (sallallaahu alayhi wa sallam).
You do not try to find out the why and the reasoning behind things or look at man made Usuul and then reject one haidth in favor of another because it opposes your Madhhab.
You follow every hadith in context.
You remain silent and attentive for the sermon.
You pray the two Rak'ah to greet the masjid when you come in and the khatiib is giving the sermon.
This is Islaam. You submit to what Allaah and His Messenger (sallallaahu alayhi wa sallam) say and not the opinions of fallible men.
It is not for a believer to have any opinion after Allaah and His Messenger (sallallaahu alayhi wa sallam) have decreed a matter.
It is not for a believing man or a believing woman, when Allah and His Messenger have decided a matter, that they should [thereafter] have any choice about their affair. And whoever disobeys Allah and His Messenger has certainly strayed into clear error.
[Qur'aan 33:36]
This Ummah is a mess because it abandons the ways of the Messenger of Allaah (sallallaahu alayhi wa sallam) for incorrect views of men who themselves would declare themselves free of you if they found out that you rejected an authentic hadith for their incorrect fataawaa.