We believe, before Prophet Muhammad (peace be upon him), The Jews, Christians, and Sabeans (Who were following original teachings of their prophets, such as belief in Islamic monotheism, and the day of judgement, with all their laws for them) were in Islam, So they will be rewarded.
Note that, Allah first says about "who believed", indicating the people now believed in Muhammad (pbuh) , and (answering the question immediately, "what about the people before him?"), who are
Jews or Christians or Sabeans [before Prophet Muhammad]
and who have also the quality of
believed in Allah and the Last Day and did righteousness
will be rewarded. It doesn't imply that, the people who do not embrace Islam after prophet Muhammad (Pbuh) will be rewarded.
As Prophet Muhammad (Sall-allahu-alaihi-wa-sallam) says, in several hadith,
"He who dies without associating anything with Allah will enter Jannah, and he who dies associating partners with Allah will enter the Fire" source
Here, The prophet Muhammad (pbuh) clearly says that, Anyone who dies associating partners with Allah, will enter into the Fire. This is true for the current (it is for the purpose of answer, not an attack on them) Jews and Christians, who associates partners with Allah.
Second point here is, Though the fundamental belief was same from time to time, the Shariah (Law) was changed, and the later people are obliged to follow the new Shariah. And in this point, Islam is the last Shariah from Allah, and the former believers (we do not saying about people who associate with Allah, since they are filtered in the first point) have to follow and embrace the last Shariah, to be considered as the true servant of Allah. Who fail to follow, they will be excluded from the reward.
As prophet Muhammad (pbuh) says
Narrated Abu Huraira: Allah's Apostle said, "All my followers will enter Paradise except those who refuse." They said, "O Allah's Apostle! Who will refuse?" He said, "Whoever obeys me will enter Paradise, and whoever disobeys me is the one who refuses (to enter it). source
As in this Hadith Prophet Muhammad (PBUH) clearly saying
وَالَّذِي نَفْسُ مُحَمَّدٍ بِيَدِهِ لاَ يَسْمَعُ بِي أَحَدٌ مِنْ هَذِهِ الأُمَّةِ يَهُودِيٌّ وَلاَ نَصْرَانِيٌّ ثُمَّ يَمُوتُ وَلَمْ يُؤْمِنْ بِالَّذِي أُرْسِلْتُ بِهِ إِلاَّ كَانَ مِنْ أَصْحَابِ النَّارِ
By Him in Whose hand is the life of Muhammad, he who amongst the community of Jews or Christians hears about me, but does not affirm his belief in that with which I have been sent and dies in this state (of disbelief), he shall be but one of the denizens of Hell-Fire. source
The meaning of the Ayat is:
The people, who were believers in Islamic monotheism (do not associates any partner with Allah, and have belief in Last day) in their age, and follower of the Shariah (Law) revealed to them by their prophets, and died in that state, and the believer in present (Muslims in short) will be rewarded, if they did rightful deeds.
Who are excluded
- The people who associates any partner to Allah, currently ...
- The people who have believe in Allah's oneness, do not associate any partner to him, but also do not follow the last Shariah (Law) and do not accept and believe in the prophet Muhammad (pbuh), they are excluded.
Please note that, I have answered this according to my knowledge. It should not be used as the last proof for something. You can go to the Ulama (Knowledgeable person) to understand more clearly.