I read that Jews believe that when the Messiah comes he will allow pig and other food which is forbidden to them. Jesus the Messiah has already come and he confirmed the Law of Moses (Qur'an and Matthew 5:17-20) not abolished / relaxed it. Further, when he returns as a follower of Islam (and not in the capacity of a Prophet) he will "kill the pig" (hadith) meaning he will correct the Christian misunderstanding of them eating the pig and non-kosher food and confirm that pig and non-kosher food was never allowed. So Jews must have a wrong idea then that the Messiah (in his first coming) will relax these food laws? See: https://judaism.stackexchange.com/questions/55141/is-it-possible-that-judaism-would-one-day-allow-eating-pork
I'd suggest reading the answers on Judaism.SE more thoroughly. "Jews believe that when the Messiah comes he will allow pig" seems to be a sweeping generalization and a misstatement. What they say is that it is an opinion, and that it means that the pig will change its nature.
Our view, as I understand it, is that the food forbidden in the shariah of Bani Israel were of two categories:
خبايث (Khabaith) in whom the prohibition, impurity and repulsion was inherent e.g carrion, blood, filth, idolatrous sacrifices, human flesh and swine etc.
طيبات (Tayyibat) which are inherently "good" and pure things but were forbidden to them either:
because they imposed the prohibition on themselves and this became commanded to them:
كُلُّ الطَّعَامِ كَانَ حِلًّا لِّبَنِي إِسْرَائِيلَ إِلَّا مَا حَرَّمَ إِسْرَائِيلُ عَلَىٰ نَفْسِهِ مِن قَبْلِ أَن تُنَزَّلَ التَّوْرَاةُ
All food was lawful to the Children of Israel except what Israel had made unlawful to himself before the Torah was revealed.
or the Israelites were punished for their rebelliousness:
فَبِظُلْمٍ مِّنَ الَّذِينَ هَادُوا حَرَّمْنَا عَلَيْهِمْ طَيِّبَاتٍ أُحِلَّتْ لَهُمْ
For wrongdoing on the part of the Jews, We made unlawful for them [certain] good foods (طَيِّبَاتٍ) which had been lawful to them.
وَعَلَى الَّذِينَ هَادُوا حَرَّمْنَا كُلَّ ذِي ظُفُرٍ ۖ وَمِنَ الْبَقَرِ وَالْغَنَمِ حَرَّمْنَا عَلَيْهِمْ شُحُومَهُمَا إِلَّا مَا حَمَلَتْ ظُهُورُهُمَا أَوِ الْحَوَايَا أَوْ مَا اخْتَلَطَ بِعَظْمٍ ۚ ذَٰلِكَ جَزَيْنَاهُم بِبَغْيِهِمْ ۖ وَإِنَّا لَصَادِقُونَ
And to those who are Jews We prohibited every animal of uncloven hoof; and of the cattle and the sheep We prohibited to them their fat, except what adheres to their backs or the entrails or what is joined with bone. [By] that We repaid them for their injustice. And indeed, We are truthful.
Or the prohibition wasn't in the Torah originally but was derived or adopted by their Prophets and Rabbis as caution i.e Rabbinic laws.
It was prophesied to them that all the طيبات (Tayyibat) would be made lawful by the final Messenger:
لَّذِينَ يَتَّبِعُونَ الرَّسُولَ النَّبِيَّ الْأُمِّيَّ الَّذِي يَجِدُونَهُ مَكْتُوبًا عِندَهُمْ فِي التَّوْرَاةِ وَالْإِنجِيلِ يَأْمُرُهُم بِالْمَعْرُوفِ وَيَنْهَاهُمْ عَنِ الْمُنكَرِ وَيُحِلُّ لَهُمُ الطَّيِّبَاتِ وَيُحَرِّمُ عَلَيْهِمُ الْخَبَائِثَ وَيَضَعُ عَنْهُمْ إِصْرَهُمْ وَالْأَغْلَالَ الَّتِي كَانَتْ عَلَيْهِمْ ۚ فَالَّذِينَ آمَنُوا بِهِ وَعَزَّرُوهُ وَنَصَرُوهُ وَاتَّبَعُوا النُّورَ الَّذِي أُنزِلَ مَعَهُ ۙ أُولَـٰئِكَ هُمُ الْمُفْلِحُونَ
Those who follow the messenger, the Prophet who can neither read nor write, whom they will find described in the Torah and the Gospel (which are) with them. He will enjoin on them that which is right and forbid them that which is wrong. He will make lawful for them all good things (طيبات) and prohibit for them only the foul (خبايث); and he will relieve them of their burden and the fetters that they used to wear. Then those who believe in him, and honour him, and help him, and follow the light which is sent down with him: they are the successful.
And this was fulfilled:
يَسْأَلُونَكَ مَاذَا أُحِلَّ لَهُمْ ۖ قُلْ أُحِلَّ لَكُمُ الطَّيِّبَاتُ
They ask you, [O Muhammad], what has been made lawful for them. Say, "Lawful for you are [all] good foods (طيبات)
الْيَوْمَ أُحِلَّ لَكُمُ الطَّيِّبَاتُ ۖ وَطَعَامُ الَّذِينَ أُوتُوا الْكِتَابَ حِلٌّ لَّكُمْ وَطَعَامُكُمْ حِلٌّ لَّهُمْ
This day [all] good foods (طيبات) have been made lawful, and the food of those who were given the Scripture is lawful for you and your food is lawful for them.
Now about the question of Jesus:
In the shariah given to Jesus, some prohibitions on the Israelites were relaxed. This is proven in the Quran:
وَمُصَدِّقًا لِّمَا بَيْنَ يَدَيَّ مِنَ التَّوْرَاةِ وَلِأُحِلَّ لَكُم بَعْضَ الَّذِي حُرِّمَ عَلَيْكُمْ ۚ وَجِئْتُكُم بِآيَةٍ مِّن رَّبِّكُمْ فَاتَّقُوا اللَّهَ وَأَطِيعُونِ
And [I have come] confirming what was before me of the Torah and to make lawful for you some of what was forbidden to you. And I have come to you with a sign from your Lord, so fear Allah and obey me.
One interpretation is that this means that Allah abrogated some prohibitions of the Torah in His revelation to Jesus:
فيه دلالة على أن عيسى ، عليه السلام ، نسخ بعض شريعة التوراة
This is evidence that Jesus abrogated some of the shariah of the Torah
This means part of the Tayyibat and not the Khabaith, a similitude of this is that Allah might have excused them from the Sabbath or from not eating fat, camels or mixing milk with meat ... but He wouldn't have allowed them to worship false gods or to steal, murder and rape etc.
Another interpretation is that this isn't about the prohibitions of the Torah but about other prohibitions:
قيل : إنما أحل لهم عيسى عليه السلام ما حرم عليهم بذنوبهم ولم يكن في التوراة ، نحو أكل الشحوم وكل ذي ظفر . وقيل : إنما أحل لهم أشياء حرمتها عليهم الأحبار ولم تكن في التوراة محرمة عليهم
It was said: Jesus permitted them some of what had been forbidden to them because of their sins and this was not in the Torah, such as fat and animals with undivided hoofs. And it was said that he permitted them to eat that which had been forbidden to them by their scholars and was not forbidden to them in the Torah.
In either case, this does not include pork, because the prohibition is inherent and stands even in the shariah of Muhammad:
حَرَّمَ عَلَيْكُمُ الْمَيْتَةَ وَالدَّمَ وَلَحْمَ الْخِنزِيرِ وَمَا أُهِلَّ لِغَيْرِ اللَّهِ
He has forbidden to you dead animals, blood, the flesh of swine, and that which has been dedicated to other than Allah
حُرِّمَتْ عَلَيْكُمُ الْمَيْتَةُ وَالدَّمُ وَلَحْمُ الْخِنزِيرِ وَمَا أُهِلَّ لِغَيْرِ اللَّهِ
Prohibited to you are dead animals, blood, the flesh of swine, and that which has been dedicated to other than Allah
أَوْ لَحْمَ خِنزِيرٍ فَإِنَّهُ رِجْسٌ
or the flesh of swine - for indeed, it is impure
And Allah says about this shariah:
الْيَوْمَ أَكْمَلْتُ لَكُمْ دِينَكُمْ وَأَتْمَمْتُ عَلَيْكُمْ نِعْمَتِي وَرَضِيتُ لَكُمُ الْإِسْلَامَ دِينًا
This day I have perfected for you your religion and completed My favor upon you and have approved for you Islam as religion.