Showrunner Dave Filoni discussed this in an interview with IGN. The very short answer is that the show was intended to be fun and accessible for all of Star Wars' fans, including those small number of fans (no, seriously. They do exist) who actually quite like Jar Jar.
But I think in the end, with 100 episodes of Clone Wars, no matter
what type of Star Wars fan you are -- and I think that’s something a
lot of people miss; there are a lot of types of Star Wars fans, and by
now they want different things out of the saga. Some people want it to
be like A New Hope, some people want it to be very dark. Some people
want it to not be about main characters and about side characters. You
know, everybody has a different need. Clone Wars, by the nature of the
way George had to tell the stories, covers a lot of that. So if you
just like bounty hunters, we’ve got that. If you just like Sith Lords
fighting Sith Lords, we’ve got that. Sith Lords fighting Jedi, we’ve
got that. Force gods that you never thought of, we’ve got that. Just
about R2-D2 and C-3PO, got that. If you are a holdout Jar Jar Binks
lover, we’ve got that. A whole range of clone people, we’ve got that.
There was something to satisfy everybody in the end.
Additionally, in the Bombad Jedi featurette on Starwars.com, Filoni explicitly states that George Lucas personally insisted on Jar Jar's inclusion.
Filoni: Early on, George expressed an interest that because we're in this time
period, the Clone Wars, that he wanted to see Jar Jar again and Henry Gilroy and I felt that perhaps an animated venue, like The Clone Wars is gonna fit really well for our friend, Jar Jar.
"Jar Jar Binks has been almost universally hated by audiences."
I recommend watching "Star Wars: The Phantom Menace 20 years later". In there you can find that Jar Jar is quite cherished by a long chunk of SW fans, the fans that were kids (12 at most) when Ep I came out.
So Filoni is aware of that chunk and he gave Jar Jar some redemption on those chapters.
Its unfortunate that as Jar Jar received so much hate we weren't given the chance to see his character evolve and have more focus (Jar Jar growing from outcast to senator for Naboo was quite a story. And then him asking for emergency powers for Palpatine was genius.). So I thank the Clone Wars for giving him some screen time.
To begin with, I think if the show lacked Jar Jar, it would seem off. I actually found it strange how many political episodes lacked Jar Jar, considering that in the movies he is always seen in the Naboo senatorial pod. Yes, Jar Jar was not extremely popular when the movies first came out, but the same could be said of practically every other character in the Prequels, save perhaps Obi-wan. If anything, with such a major character in The Phantom Menace, I think he should have been in it more. Since then, there are two or three characters who have almost undoubtedly landed in the territory of being less popular than Jar Jar—Rose Tico, Admiral Holdo, and (arguably) Rey "Skywalker". But certainly, in the case of Rose Tico, many objected to how absent she was from Episode IX. They probably wanted her improved. Since The Clone Wars made almost every character better from the Prequels, I don't see why Jar Jar should not receive the same courtesy of being more fleshed out—and fleshed out he was, between showing himself to be very experienced with nature, taming a giant slug, negotiating with General Grievous, and becoming Indiana Jones for one episode.
But really, I think the idea that he is "almost universally hated by audiences" is something of a myth, brought on more by a fad of what is popular to believe. Yes, some people actually do not like Jar Jar and they are free to (though I suspect most of them are the types who are not too keen on the droids either), but I get the impression that the fad came on from people quoting the media (back before social media was big) and therefore the vocal minority became the majority. Also, I suspect some of the older fans may have just been resistant because he was new and unexpected, since I find most newcomers to the Star Wars universe do not have much of an antipathy toward him.
If you want to see how people actually feel about Jar Jar, go out and ask real Star Wars fans, particularly those under the age of twenty-five. I suspect you will find a mixture of ambivalence and absolute love for the character. And if you need proof, just watch this.