The book wasn't about Islam. It also wasn't about Christianity. It was about the Dominion Theorcracy which resembles more what we see with the religious extremists in America.

Edit: I would like to add that it also fits religious extremism in Islamic countries, but that's not what the aim of the author was. She definitely meant America and their extremists. She even created a flag that looks awfully similar to the American flag.

Dominion Theology is a group of Christian political ideologies that seek to institute a nation governed by Christians based on their personal understandings of biblical law. Extents of rule and ways of achieving governing authority are varied. For example, Dominion Theology can include theonomy, but does not necessarily involve advocating Mosaic law as the basis of government. The label is applied primarily toward groups of Christians in the United States.

The red and white garb is from The Handmaid's Tale. I think the original cartoon might be suggesting that the voting booth is a chance for women to shed the garb that's representative of patriarchal oppression. Given reproductive rights are a big topic this election, I think that seems true, to an extent.

For figuring out what the twitter user was talking about, let's consider a more general interpretation of the cartoon, such as "the themes of theocratic and patriarchal oppression are relevant to this US election". It seems that they have picked up on the fact that theocratic patriarchy is a thing in the Handmaid's Tale, but they have (likely due to cognitive dissonance) concluded that the author clearly couldn't be talking about Christianity, because Christianity is Good, and they are Christian, and they are also Good, you see?

Now, I haven't actually read The Handmaid's Tale, so I don't know to what extent it is targeted allegorical criticism at Christianity. It is true that some Muslims also ascribe to (and attempt to enforce on others) a theocratic patriarchal ideology, and also the shape of this kind of oppression looks pretty similar no matter what religion is driving the theocracy — so it's certainly plausible that The Handmaid's Tale could be used to criticise theocratic patriarchal manifestations of Islam too. However, the twitter user is clearly not thinking along these lines. I think they believe that The Handmaid's Tale is aimed at Islam because it helps alleviate some of the cognitive dissonance they feel from a book that is directly criticising them. It definitely is very Christian coded though, I feel like this twitter user is so close to getting it that they're a self-awarewolf

Because certainly not all Christians are patriarchally oppressive. Some do the most progressive, compassionate people I know are Christian and they will be the first to acknowledge the argument that Christianity itself may be inherently patriarchally oppressive (as well as other kinds of oppressive). We can sort of imagine a separation, where there's an abstract "Christianity", and then there's the ways in which Christianity has been used as a tool of oppression by powerful people. I like the way my friend put it: "I really want to say that the assholes [who use Christianity as an excuse to hate and oppress others] aren't real Christians, but that feels too easy and appealing to do — denouncing them in that way doesn't feel very Christian of me, because it would allow me to ignore them. I think my duty as a Christian is to acknowledge the discomfort and be on the watch for this and challenge it where I can, especially in my own community."

TL;DR:

• the Handmaid's Tale is against religious theocracies (such as what conservatives Christians would have the world look like)
• this election is big for women's rights, which have been eroded largely by religious conservatives
• a Muslim theocratic patriarchy would look similar to the Christian version, especially considering that theocratic patriarchies aren't about religion per se, but using religion as a tool of oppression.
• thus the Handmaid's Tale can be seen as a criticism of both Muslim and Christian theocratic patriarchy, though it's obvious to most people who have read the book that it is more directly critiquing the Christian variant.
• The twitter user has (presumably) read the book and seems to have been close to "getting the point", but their xenophobia saved them from having to do some uncomfortable and difficult self reflection about their own (presumed) Christianity.