People who legitimately have a disability that affects their cognition are at increased risk of being abused and scammed. They are also more likely to not be able to afford help, especially when they need it most. Exploiting people's disabilities for personal gain is not only unethical, but arguably already illegal financial exploitation.
If a person provides a steady supply of lies and manipulation with the intention of stirring up xenophobic outrage to fill their wallet, then... yes. They do hold some responsibility for the foreseeable risk that promoting outrage inspires outrage. At best, the liar believe their own lies, in which case they still need to show their math when claiming very specific things like "crime by Muslims is being systemically under-reported". That's not just an opinion like "i don't trust Muslims" anymore, it's a quantifiable and verifiable or falsifiable claim. There are multiple laws around fraud, libel, etc. that deal with these sorts of arguments daily.
Just like we condemn phone scammers for preying on grandparents with dementia, it is very much not ok to steal from people who are ill and need real genuine help.