Traditionally activist hedge funds are, uh, hedge funds. They are privately managed pools of capital in which the investors — the limited partners — do not get much in the way of voting rights. If the investors in an activist fund do not approve of its activism, they can (probably, eventually) withdraw their money and invest it somewhere else, but they can’t, like, vote out the hedge fund’s manager and install someone else. Activist hedge funds are not generally themselves susceptible to activism.
In theory you could run an activist strategy out of, say, a mutual fund run by a publicly traded asset manager. But then someone might do an activism on you: try to replace you as manager of the fund, mount a hostile takeover of your asset-management firm, whatever. This would be embarrassing for you.