It's not really 'should', guest - the stems tend to go woody and therefore stringy when you cook them. Also, the plant needs a rest soon, so I think it's probably better not to pull any more stems.

agree, better not.

There's a story that rhubarb becomes poisonous after July but that's just a story.

It seems to come from the fact that the leaves are toxic and, as already posted, you need to give the plant a rest from July (ish). Someone put those two together and the story started that the leaf blades become toxic.