A bit much for one averagely popular TV series to achieve?
Mandy Patinkin is notably left-leaning , and a vocal opponent of the Trump government. Claire Danes is less vocal but she is a supporter of feminist causes and women's rights in Afghanistan, activities which are hardly going to endear her to the right. The show was popular with Obama and also the Clintons (yeah, OK, all of these would be considered right to centre-right over this side of the pond) which although somewhat tangential evidence and hardly conclusive, at least suggests that there's something in the show that appeals to more than the Trump rump.
My view of the whole series is that it adheres to US spy-thriller conventions, so you have to swallow a couple of precepts. Firstly, the Good Old Constitution and the American Way are basically God-ordained perfection and secondly, anybody threatening the GOC is basically bad. That said, the show did at least attempt to portray light and shade within those rules. It also delves into themes such as collusion with Russia, misuse of mass data for political ends etc. etc.
Yes, it reinforces lazy stereotypes of Arab nations and other Islamic countries. It's amusing that Arab grafitti artists hired to add authenticity to the set of a refugee camp in fact put up slogans that 'Homeland is racist' and 'a watermelon' (sham, fake). I suppose that's the big problem. It doesn't matter that the producers were well-meaning if they were also lazy enough to accept and perpetuate the narrative that all of the Islamic world is essentially a rabid hell on earth and that the West had no hand in creating the problems that afflict it.
Pity that two very fine performances are buried in here.