The idea of something like this happening anywhere else in the world, even in 1851, seems insane.
How did a Chinese man convince millions of people he was the sibling of Jesus and son of God, and to take up arms against the chinese Emperor?
Was this a case of people already looking to rebel merely backing the first cause that had appeared, or did so many people truly believe he was who he claimed to be?
This series of posts about the religion of the heavenly kingdom, by u/EnclavedMicrostate, in the askhistorians wiki is a very high quality answer on the what the taiping rebellion was about and how it grew so large.
I've recently answered a question on the sincerity of Taiping belief here, but this is a somewhat broader-ranging question so it does deserve a distinct answer of its own. The exact reasoning behind people's support from the Taiping was far from universal, and different supporters did so for different reasons, particularly if we distinguish between the pre-uprising phase, when the Taiping were still just the God-Worshipping Society, a sectarian organisation based in Guangxi and numbering no more than 50,000, and the post-uprising phase, when the Taiping were actively challenging the empire and there were indeed 'millions' of supporters. That is not to say that people had wildly different reasons for their involvement before and after the declaration of the Heavenly Kingdom, as I'd say that in both cases there was a mixture of genuine belief in the new doctrines in conjunction with broader existing concerns on which the Taiping capitalised, however it is hard to deny that the religious side appears to have been more significant during the earlier period and the pragmatic side during the later.
Of course, the God-Worshippers and Taiping shared the same religious doctrines, and both operated as simultaneously pro-peasant and anti-elite organisations, but the actual modus operandi differed between the two quite heavily, the former being a sectarian secret society and the latter an outright rebel state. As such, the ways in which the religion was spread and the ways in which inter-class activities manifested were also distinct, as was the recruitment process. The God-Worshippers, like any sectarian organisation, were able to send proselytisers out to various towns and villages to establish houses of worship and gain members, with risk of suppression but not outright persecution. Combatting banditry and assisting local peasants against elite abuses provided pragmatic reasons for locals to join, of course, but I do have reason to believe there was a strong religious current involved, as at least 30,000 people had joined up with the God-Worshippers by 1851, despite the existence of several alternative organisations with less prohibitionist tendencies. Of 10 river pirate chiefs identified as having associated with the God-Worshippers, only two, Luo Dagang and Su Sanniang, stayed on long-term, whilst the rest either deserted or even outright defected, with the rather amusingly named 'Big-Headed Yang' being a notable example of the latter. Moreover, that the God-Worshippers were able to grow so rapidly without forming an alliance with the more well-established Triads (a.k.a. Heaven and Earth Society) is particularly indicative of how the God-Worshippers had a distinctive appeal rather than just being the only group to exploit unstable conditions.
By contrast, the Taiping Heavenly Kingdom no longer had the ability to operate openly outside its own borders, but had far more authority than it had previously had as the God-Worshippers within them. Qing records indicate that the dissemination of tracts and pamphlets to cities and market towns outside Taiping control was rife, but the presence of outright provocateurs and evangelists is unattested, and may to some extent explain why there was a lack of spontaneous sympathetic uprisings, despite the broadly positive reception of Taiping armies when they actually did arrive in a region. The absence of known popular counter-insurrections in Taiping territory could be taken as a sign that there was little popular resistance to the new doctrines, although that is not by any means unequivocal proof that those in Taiping territory were devout believers. I would contend, moreover, that the fact that the anti-elite message of the Taiping survived for so long (with popular appeals to the Taiping legacy well into the Mao era) and so widely, from Sichuan to Shandong to Guangdong, suggests that it was very much the pragmatic side that had broader appeal at the national level.
As for whether they were simply 'merely backing the first cause that had appeared', that such a motive may have applied to some is hard to deny. With the Taiping transitioning from being merely one of many minor sects and support organisations in Guangxi to a rebel state in a full-on shooting war with the Qing, many had to make a choice. For all but the most philanthropic of the elite, whose status was actually threatened by both sides but to different degrees, the Taiping were undoubtedly the greater of two evils, and they chose to throw their lot in with the Qing. However, what is notable is that around 200,000 of the residents of the Taiping capital at Nanjing, in the northwest of Jiangsu Province, were from Hubei or Hunan, even though the Taiping only passed through these provinces in 1853 and had only limited control over the former on the banks of the Yangtze. It's not difficult to infer from this that the Taiping did have broad enough appeal to induce people to migrate from their home provinces in quite substantial numbers – at a time of quite strong provincialism no less – in support of them.
Yet these people seem more than a little like the exception rather than the rule. We often hear stories of those living on the edges of Taiping rule who would grow their hair out in the Taiping manner, but keep the normal queue braided just in case so that they could shave the rest off in the event of a Qing recapture of their area, and defections of mid-level military leaders could be quite common, at least for newer recruits. Chen Yucheng's capture and execution in 1862 was the result of one such defection of a recently-acquired ally, whilst the fall of Suzhou in 1863 occurred when the (admittedly already demoralised) subordinate commanders turned on their general and struck a deal with the British commander of the Anhui Army's vanguard contingent, the Ever-Victorious Army. Whilst there appears to have been an atypically high amount of popular support for the Taiping, it would not be unreasonable to say that the modal opinion may still have been ambivalence, even if there was a generally pro-rebel mean.
Sources, Notes and References:
I will gladly give specific references if asked, but I include a general bibliography below.