I will quote an excerpt from the Commentary of the Qur'an on verse 2:144 from Abdullah Yusuf Ali. He has explained this question of yours, which I have not seen answered in any other commentary (at least from the available English ones I have access to, which is quote a lot actually).
He wrote:
"...Until the organization of his own people into a well-knit community, with its distinctive laws and ordinances, he followed a practice based on the fact that the Jews and Christians looked upon Jerusalem as a sacred city. But there was no universal Qibla among them. Some Jews turned towards Jerusalem, especially during the Captivity, as we shall see later. At the time of our Prophet, Jerusalem was in the hands of the Byzantine Empire, which was Christian..."
This is an excerpt of what he wrote on this verse, but it is the only relevant portion in response to your question, I believe. Thus, the Holy Prophet (saw) did not face Jerusalem to please the Jews. Perhaps it helped to convert many of them at first, but those who hated the change in the Qibla were exposed for their hidden hypocrisy because they showed their dislike for this Divine Command from Allah.
Of course, it is still the fact that the facing in the direction of Jerusalem as a Qibla. It is unlikely that the Holy Prophet (saw) tried to please the Jews by facing the direction of Jerusalem. Even if at one point the Holy Prophet (saw) thought this way about the Qibla being Jerusalem (and Allah knows best in the end), then Allah admonished him about trying to please both the Jews and the Christians in the Holy Qur'an:
2:120 Never will the Jews nor the Christians be pleased with you (O Muhammad صلى الله عليه وسلم) till you follow their religion. Say: "Verily, the Guidance of Allah (i.e. Islamic Monotheism) that is the (only) Guidance. And if you (O Muhammad صلى الله عليه وسلم) were to follow their (Jews and Christians) desires after what you have received of Knowledge (i.e. the Qur'an), then you would have against Allah neither any Wali (protector or guardian) nor any helper.
Furthermore, the above excerpt mentions that the facing was towards Jerusalem as a sacred city, not at the temple itself specifically. To be honest, I did not know that until now myself. So I should thank you for helping me to be more guided in this by researching more on this issue and being more clarified in my understanding of it.
And since Mecca and both Jerusalem were in a state of evil behavior (I am not sure if apostasy was the only issue), then the only conclusion is that the facing is towards a sacred center in general. Jerusalem is considered pretty eminent by Muslims since the Isra of the Holy Prophet (saw) entailed him traveling to Jerusalem from Mecca. There is no doubt that the city itself is sacred. In fact, Jerusalem is considered holy because it has the sacred site of the "Furthest Mosque" which is mentioned in verse 17:1
17:1 Glorified (and Exalted) be He (Allah) [above all that (evil) they associate with Him] Who took His slave (Muhammad صلى الله عليه و سلم) for a journey by night from Al-Masjid-al-Haram (at Makkah) to Al-Masjid-al-Aqsa (in Jerusalem), the neighbourhood whereof We have blessed, in order that We might show him (Muhammad صلى الله عليه و سلم) of Our Ayat (proofs, evidence, lessons, signs, etc.). Verily, He is the All-Hearer, the All-Seer .
But in order to fully satisfy your answer, you should know that the sacred site in Jerusalem is the later completed Masjid Al-Aqsa which was finished in A.H 68. Abdullah Yusuf Ali write under this verse the following (an excerpt):
"The Farthest Mosque must refer to the site of the Temple of Solomon in Jerusalem on the hill of Moriah, at or near which stands the Dome of the Rock, called also the mosque of Hadrat 'Umar. This and the Mosque known as the Farthest Mosque (Al-Masjid-ul-Aqsa) were completed by the Amir 'Abd-ul-Malik in A.H. 68. Farthest, because it was the place of worship farthest west which was known to the Arabs in the time of the Prophet; it was a sacred place to both Jews and Christians, but the Christians then had the upper hand, as it was included in the Byzantine (Roman) Empire, which maintained a Patriarch at Jerusalem."
The mosque itself is not necessarily the Qibla in Jerusalem. This is not what I mean. But, the Muslims simply followed the practice of the Jews and Christians until their own law fully developed. Facing Jerusalem remained part of the Divine Command until Allah told the Muslims otherwise. As I explained earlier, the reasons for this are that there were prophecies reported by the early Muslim scholars which the Jews had that showed this trait amongst the Prophet who would be raised in Arabia. For good reason too. If you think about it, the line of Prophethood for the Prophets through Ishaq (as) (that is, Isaac) finished, and the line of Prophethood was still left for the Ishmaelites, who would have the final Prophet of Allah. Thus, this changing of Qibla is in a way a metaphorical sign of the changing of this line of prophethood since the prayers offered were at the house which Ishmael (as) and Ibrahim (as) built and prayed at its completion that the people of that particular city should have a Prophet to guide them to the ways of worship. And that worship was specifically referring to being towards that particular House of Allah - the Ka'ba.
So, the Jews rejecting the Messiah has nothing to do with the facing towards Jerusalem, nor does it affect anything here in any way, except that that itself was one of the causes for the disruption of Prophethood in the line of Ishaq (as). But this is mere speculation on my part about those effects. Allah knows best in the end.
Let me know if you have any more questions. i hope this helped answer some of them for you.
