The Quran says that the Torah and the Gospel say that the people should follow Muhammad ﷺ:
الذين يتبعون الرسول النبي الأمي الذي يجدونه مكتوبا عندهم في التوراة والإنجيل ... فالذين آمنوا به وعزروه ونصروه واتبعوا النور الذي أنزل معه أولئك هم المفلحون
Those who follow the Messenger, the unlettered prophet, whom they find written in what they have of the Torah and the Gospel ... So they who have believed in him, honored him, supported him and followed the light which was sent down with him - it is those who will be the successful.
— Quran 7:157
It also mentions that Allah made a covenant with the Bani Israel, which included the command to believing in the Messengers, and Muhammad ﷺ is included in the Messengers:
ولقد أخذ الله ميثاق بني إسرائيل ... وقال الله إني معكم لئن ... وآمنتم برسلي
And Allah had already taken a covenant from the Children of Israel ... "I am with you. If you ... believe in My messengers ..."
— Quran 5:12
So how can they follow their own law without accepting Islam? It is an absurd idea. Rather accepting Islam is what following their own laws entails.
To each of you We prescribed a law and a method.
Meaning that to your ancestors from the Bani Israel, Allah prescribed the laws of the Torah and the Gospel. These laws were at times different from the laws of the Quran, for example the Sabbath and some of the laws regarding food etc.
Had Allah willed, He would have made you one nation
Meaning that had Allah willed He would prescribed the same set of laws for all time from Adam عليه السلام to Muhammad ﷺ.
It could also mean that had Allah willed He would have guided you all.
but [He intended] to test you in what He has given you;
Meaning that He prescribed different laws at different times as a means of testing the people.
so race to [all that is] good.
This command is addressed to the current people. To the Ummah of Muhammad ﷺ to compete with the previous nations and to try to exceed the standards set by them.
And also to the Bani Israel of the present time that they should accept Islam and race towards other good deeds. Remaining on their old laws and disbelieving in the creeds of Islam is not "good" rather it is disbelief, disobedience and breaching the covenant of Allah.
He will [then] inform you concerning that over which you used to differ
Allah will inform you regarding your differences, meaning that He will judge between the believers and disbelievers among you.