British tolerance of non-Anglican religions in politics in the 19th Century was fairly complicated and had a number of progressive reforms, though could hardly be considered liberal in modern times. You might find it useful to compare to 'Don't ask, don't tell' in the military. Disraeli was able to 'climb the top of the greasy pole' because of changing laws and attitudes, an upwardly thinking father, and his own political scheming.
If you're not aware, the official religion of Britain was (and still is) Church of England, also known as Anglicanism. Legally, Dissenters/Non-Conformists (non-Anglican Protestants), Catholics, and Jews were all restricted to varying degrees. Until the late 1700s, for example, a Catholic father could not leave his entire estate to one son unless that son converted to Anglicanism. All of these religions were officially forbidden from entering public office, lest they use this power to undermine the established religion. The main mechanism for this was the use of a Sacramental Test; before taking office, you had to take communion in an Anglican way (similar to swearing on the Bible before being in court).
In reality, however, by the early 1800s, these tests were not uniformly applied, even for MPs, so Dissenters were tolerated in public office. The Sacramental Tests Act 1828 officially allowed them, followed by Catholic Relief Act 1829, and Jewish Relief Act 1858. Moreover, Disraeli himself did not experience severe obstacles through anti-semitism. In fact, in the intellectual and literary circles that he preferred to be in, his Jewish heritage was seen as somewhat charming and interesting. This is not to say that either the average man or average voter approved of Jews, but an example of 'progressive' British attitudes towards Judaism in this period. I genuinely don't know to what extent this was anti-Semitic rather than a general nationalism/fear of the other. For decades after Catholic Emancipation, MPs were expected to run for election again if they converted to Catholicism to test whether their constituents accepted this.
In any case, as an essentially self-made man, Disraeli was helped by familiarity in these circles for a large source of his income (even though the stress of reactions to his first book resulted in him suffering a mental breakdown). During one particularly bad spot when the debtors were looming in the 1840s, he wrote a trilogy of relatively successful novels. After his first spell as Prime Minister, he wrote 'Lothair', and received an advance of £10,000, an amount of money so large it was said that only Dickens could have expected more. (He also married a rich widow, but that's not too relevant to this q...) All this suggests that, given the right circumstances, people were more than willing to tolerate and even support people of Jewish birth.
More importantly, Disraeli was only Jewish by birth, not by practice. His father was not a true believer in Judaism, and had converted the family to Anglicanism, sensing that they would have better life chances. Benjamin took this a step further, anglicising his last name from D'Israeli to Disraeli. However, he never abandoned his Jewish roots, having had at least a cultural awakening on his Grand Tour visiting Jerusalem. He wrote several books both explicitly and implicitly supporting elements of Judaism, though he was also complimentary of the Church of England. The point remains that with shifting attitudes, and no record of actual Jewish belief, Disraeli faced no legal barriers to entering Parliament in 1837, decades before the Jewish Relief Act.
Finally, Disraeli was simply very good at politics, and very ambitious. As he once publicly confessed: “I love fame; I love public reputation; I love to live in the eyes of the country; and it is a glorious thing for a man to do who has had my difficulties to contend against.” He was a firm believer in oppositional politics - opposing your opposition's ideas and policies simply for the benefit it gave you, rather than because they were genuinely bad ideas. The key example is his championing of protectionist tarrifs on British food. The Conservative leader at the time, Robert Peel, repealed the Corn Laws in 1846 for a variety of reasons, but this was deeply unpopular amongst his own landowning backbenchers. Disraeli ruthlessly exploited this, becoming the leader of a massive backbench revolt, forcing Peel to resign in the same year. Years later, once Disraeli was in a firmer position, he shrugged off any support for protectionism. His books also helped weave a political narrative that attracted support. The trilogy of books I mentioned are partly used even today as the basis of 'One Nation Conservatism', which roughly supports civil and religious institutions and socioeconomic reforms for the common man. His support of the 1867 Reform Act enfranchised a lower rung of respectable working class voters. All of these were designed to consolidate his support both within and without of Parliament. The latter didn't largely work, as his first premiership was only around 9 months in 1868, but he did return from 1874-80. A final point worth mentioning is that he completely charmed Queen Victoria, who considered him one of the two most favourite PMs who ever served her in 64 years. This public support doubtless dulled the edge of any anti-semitic opposition Disraeli could have publicly faced after his first premiership.
Hope this answers your question!
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