Praise be to Allah, and peace and blessings be upon the Messenger of Allah and his family.
Firstly:
It was narrated by at-Tirmidhi (812), at-Tabari in his Tafseer (6/41), al-Bazzaar (861), al-Bayhaqi in ash-Shu‘ab (3692) and Ibn al-Jawzi in al-Mawdoo‘aat (2/209) via Hilaal ibn ‘Abdullah, the freed slave of Rabee‘ah ibn ‘Amr ibn Muslim al-Baahili, who said: Abu Ishaaq al-Hamdaani told us, from al-Haarith, from ‘Ali who said: The Messenger of Allah (blessings and peace of Allah be upon him) said: “Whoever possesses provisions and a mount that would enable him to reach the House of Allah, but does not do Hajj, it would not matter if he dies as a Jew or a Christian, because Allah says in His Book (interpretation of the meaning): “And Hajj (pilgrimage to Makkah) to the House (Kabah) is a duty that mankind owes to Allah, those who can afford the expenses (for one’s conveyance, provision and residence)” [Aal ‘Imraan 3:97].
At-Tirmidhi said, immediately after narrating this hadith: This is a ghareeb hadith; we only know it via this isnaad, and there are some reservations about its isnaad. Hilaal ibn ‘Abdullah is majhool (unknown), and al-Haarith was regarded as da‘eef (weak) in hadith. End quote.
Al-Bukhaari said of this Hilaal that he was munkar al-hadith (his hadith is odd). At-Tirmidhi said: He is majhool (unknown). Ibn ‘Adiyy said: He is known for this hadith, but it is not mahfooz (i.e., it is not found with anyone else). Al-Haakim Abu Ahmad said: He is not qawiy (strong) in their view.
Tahdheeb at-Tahdheeb (11/82)
Al-Haarith is al-Haarith ibn ‘Abdullah al-A‘war, who is well known to be da‘eef. He was regarded as a liar by ash-Shu‘bi and Ibn al-Madeeni. See: at-Tahdheeb (2/145)
The hadith has other isnaads, all of which are not free of weakness.
This hadith was classed as da‘eef by more than one of the scholars. It was classed as da‘eef by at-Tabari in his Tafseer (6/45); Ibn al-Jawzi in al-Mawdoo‘aat (2/210); al-Mundhiri in at-Targheeb wa’t-Tarheeb (2/137); Ibn ‘Abd al-Haadi in at-Tanqeeh (3/404); and al-Haytami in az-Zawaajir (1/330). It was narrated that an-Nawawi classed it as da‘eef, and al-Albaani also classed it as da eef in Da‘eef at-Tirmidhi.
But there is a similar report that is soundly attributed to ‘Umar (may Allah be pleased with him). Ibn Katheer (may Allah have mercy on him) said:
Abu Bakr al-Ismaa‘eeli al-Haafiz narrated from the hadith of Abu ‘Amr al-Awzaa‘i: Ismaa‘eel ibn ‘Ubaydullah ibn Abi’l-Muhaajir told me: ‘Abd ar-Rahmaan ibn Ghanm told me that he heard ‘Umar ibn al-Khattaab say: Whoever is able to do Hajj but does not do Hajj, then it is all the same whether he dies as a Jew or a Christian. This is a saheeh isnaad going back to ‘Umar (may Allah be pleased with him). End quote.
Tafseer Ibn Katheer (2/85)
Secondly:
It was narrated by ad-Daarimi (1826), al-Bayhaqi in ash-Shu‘ab (3693), Abu Nu‘aym in al-Hilyah (9/251), and Ibn al-Jawzi in at-Tahqeeq (2/118), via Shareek, from Layth, from ‘Abd ar-Rahmaan ibn Saabit, from Abu Umaamah who said: The Messenger of Allah (blessings and peace of Allah be upon him) said: “Whoever is not prevented from doing Hajj by genuine need, an oppressive ruler or debilitating sickness, and dies without having done Hajj, let him die if he wishes as a Jew or if he wishes as a Christian.”
This is a da‘eef (weak) isnaad. Layth – who is ibn Abi Saleem – is da‘eef. He was classed as da‘eef by Ahmad, Ibn Ma‘een, an-Nisaa’i and others. See: al-Mizaan (3/420).
Shareek – who is ibn ‘Abdullah al-Qaadi – is also da‘eef and had a poor memory. He was classed as da‘eef by al-Qattaan, Ibn al-Mubaarak, Ibn Ma‘een, al-Jawzjaani, and others.
See: al-Mizaan (2/270)
Abu’l-Ahwas Sallaam ibn Sulaym differed with him. He narrated it from Layth, from ‘Abd ar-Rahmaan ibn Saabit, who said: The Messenger of Allah (blessings and peace of Allah be upon him) said… and he quoted it as a mursal report. This was narrated by Ibn Abi Shaybah (3/305).
It was also narrated from Layth by ath-Thawri, as reported by al-Khallaal in as-Sunnah (5/46)
This is more sound, but it is also da‘eef, because of the weakness of Layth and because it is mursal.
Al-Haafiz Ibn Hajar (may Allah have mercy on him) said:
Layth is da‘eef and Shareek had a poor memory. Sufyaan differed with him and narrated it in a mursal report. It was narrated by Ahmad in Kitaab al-Eemaan from Wakee‘ from Sufyaan from Layth from Ibn Saabit who said: The Messenger of Allah (blessings and peace of Allah be upon him) said: “Whoever dies without having done Hajj and was not prevented from doing it by debilitating sickness or an oppressive ruler or genuine need…” He narrated it as a mursal report. It was also narrated by Ibn Abi Shaybah from Abu’l-Ahwas from Layth in a mursal report. End quote.
At-Talkhees al-Habeer (2/486)
This report has other isnaads from Shareek. Ibn al-Jawzi said in at-Tahqeeq (2/118):
It was narrated by ‘Ammaar ibn Matar, from Shareek, from Saalim, from Abu Umaamah. Al-‘Uqayli said: ‘Ammaar narrates munkar reports from trustworthy narrators. Ibn ‘Adiyy said: He is matrook al-hadith (his hadith is to be ignored). End quote.
Al-Haafiz Ibn Hajar (may Allah have mercy on him) said:
It was narrated by Abu Ya‘la via other isnaads from Shareek, that are different to the first isnaad. Its narrator from Shareek is ‘Ammaar ibn Matar, who is da‘eef. End quote.
At-Talkhees al-Habeer (2/486).
Ibn al-Qaysaraani said:
It was narrated by ‘Ammaar ibn Matar ar-Rahhaawi from Shareek, from Mansoor, from Saalim ibn Abi’l-Ja‘d, from Abu Umaamah, but this is not known by anyone else. The problem with it stems from ‘Ammaar ar-Rahhaawi. End quote.
Dhakheerat al-Huffaaz (4/2407)
This ‘Ammaar is Abu Haatim ar-Raazi, who used to tell lies. Ibn ‘Adiyy said: His hadiths are false.
Mizaan al-I‘tidaal (3.170)
Ibn al-Qaysaraani said:
It was narrated by Nasr ibn Muzaahim al-Kufi from ath-Thawri, from Layth, from Ibn Saabit, from Abu Umaamah. This is not known by anyone else. The problem with it stems from this Nasr. End quote.
Dhakheerat al-Huffaaz (4/2407)
Concerning Nasr ibn Muzaahim, adh-Dhahabi said in al-Mizaan (4/253): He is a Raafidi fanatic; they dismissed his hadith.
It was narrated by Abu’l-Hasan an-Ni‘aali in his Juz’ (71) via Muhammad ibn ‘Abdullah al-Ashnaani: Ahmad ibn Hanbal told us: Muhammad ibn Ja‘far told us: Shu‘bah told us, from Simaak ibn Harb, from ‘Abd ar-Rahmaan ibn ‘Abdullah ibn Mas‘ood, from his father, in a marfoo‘ report.
Concerning this al-Ashnaani, ad-Daaraqutni said: He was a charlatan. Al-Khateeb said: He used to fabricate hadith. Lisaan al-Mizaan (5/228).
Concerning an-Ni‘aali, the author of al-Juz’, al-Khateeb said: He was a Raafidi who would seek out strange and odd reports. Tareekh Baghdad (5/383).
In conclusion: the two hadiths are not sound.
And Allah knows best.