The example with the antisemite is probably more complicated, if you wanted a discussion on it you should have posted a link to the relevant discussion on Wikipedia, but I very much doubt it would be appropriate to take Twitter as source in that case, because Wikipedia is not meant to be (an extension of) social media. Also, it seems like you are not aware that it is very much possible to be a pro-Israel antisemite, e.g., the Nazis at one point supported Jewish Zionist emmigration to Palestine.
BTW, I am not a Wikipedia apologist, see my next comment.
It is true that low quality journalism limits Wikipedia in certain areas, but also note that good Wikipedia sources are not limited to newspapers, see: https://en.wikipedia.org/wiki/Wikipedia:Verifiability#Reliab...