"Laser-beam" divestment from a specific company - such as Caterpillar, which is letting the government of Israel use its products explicitly for the demolition of human rights (in the physical form of homes) - is not necessarily anti-Semitic or hostile to the existence of Israel in itself.
However, some calls for using boycotts or divestment as pressures on Israel have quickly degenerated into becoming anti-Semitic or anti-Israel-as-a-society, falling into the rhetoric of "Israel is totally wrong/the Jews are totally wrong." For example, in the discussions of the original Presbyterian decision to explore (not call for) a divestment from maybe only one U.S. company, Caterpillar, much of the Left instantly trumpeted "Presbyterians will divest from Israel."
But interestingly, so did parts of the official American Jewish establishment. It was as if there were a de facto conspiracy between the two political groupings to define any critique of a specific Israeli action, or even any specific action of a company doing business with Israel, as an attack on Israel itself, as a society.
Many calls for divestment, even from specific companies, have used the rhetoric that divestment from South African apartheid is the model - not, for instance, the boycott of nonunion California grapes a generation ago. The grape boycott helped change policy precisely because it did not try to delegitimize a whole society. Neither the pro-union nor pro-employer public lost its head or hardened its heart.