From what I've read Jews were only really emancipated in the UK around the 1830's, and European society remained broadly antisemitic until after WW2. Did Disraeli have to overcome a lot of prejudice or was the English political establishment relatively progressive in this regard?
I'm also curious if foreign leaders took issue with it (apparently Bismarck affectionately referred to him as "der alte Jude", which at least suggests it was a defining characteristic) or if his Jewishness was used in propaganda.
Benjamin Disraeli had an interesting relationship with his Jewish roots, as did the rest of Britain. So, firstly, he was a practicing Anglican from the age of twelve, married to a member of the Christian aristocracy, and as a novelist published books that reinforced social boundaries (the plot of Sybil features a working-classic daughter of a Chsrtist fall for a young aristocrat, this is only resolved when she discovers that her long lost mother was an aristocrat all along.)
In Britain at the time most people's experience of Jews, and most subsequent stereotypes, were of Ashkenazi immigrants from Russia, Germany, and Poland. These are distinct ethno-linguistic group from the southern-European Sepphardi - Disraeli's father was Sepphardi. In Mayhew's London Labour and the London Poor he interviews (or claims to interview - it is a highly embellished account intended for middle class gawking, not sociology) a young Ashkenazi Jewish boy living in the East End. The boy claims to have heard of Disraeli and quotes 'I wish he was my uncle', but Mayhew drives the point that this wave of recent Russian immigration (that most anti-Semites were particularly concerned about) were not the educated and genteel Sepphardi business owners of the West End. He has a great deal to say on London's Jewry, most of it very offensive, but that's the only mention of the prime minister.
For his relationship, he renounced Judaism as a child and was for all intents and purposes as Christian as any other MP. He also greatly re-wrote his family tree, claiming his father was descended from a line of Venetian statesmen - and overlooking that his mother actually was related to the Rothschilds. This also worked to reinforce his link to an established (and fictional) dynasty of valued royal advisors, and distanced himself from his mother's Ashkenazi roots. This played well to the new-immigration fearing anti-Semitic voters, and reinforced himself as a favourite of Queen Victoria.
Which leads us to the political climate of the time - Disraeli headed the royalist, conservative, and pro-Empire Conservative Party as a member of the ruling class, not as a former Jew. He'd been a lawyer, a stock dealer, he'd published novels about the importance of class, and he was loved by the Queen. Yet he also supported election reform (Sybil is, in many ways, a rectifying of the aristocracy and the Chartists), and protectionism of British industry. He had well-publicised affairs and attended society parties - compared to Gladstone he was an exciting new mood in Westminster, despite being a career politician and professional social climber.
That's not to say that his heritage didn't hurt him in politics, it certainly did. It was used as an attack by his political rivals occasionally throughout his career. But racial attacks are a part of politics - we still see that today - and all the Victorian MPs with Jewish or Irish heritage became experts at deflecting it.