Are scientists morally responsible for the uses of their work? To some extent, yes. Scientists are responsible for both the uses that they intend with their work and for some of the uses they don't intend. This is because scientists bear the same moral responsibilities that we all bear, and we are all responsible for the ends we intend to help bring about and for some (but not all) of those we don't.
To not think about plausible unintended effects is to be negligent -- and to recognize, but do nothing about, such effects is to be reckless.
It should be obvious that the intended outcomes of our work are within our sphere of moral responsibility. If a scientist intends to help alleviate hunger (by, for example, breeding new drought-resistant crop strains), and they succeed in that goal, they are morally responsible for that success, and we would praise them accordingly. If a scientist intends to produce a new weapon of mass destruction (by, for example, developing a lethal strain of a virus), and they are unfortunately successful, they are morally responsible for that as well, and we would blame them accordingly. Intention matters a great deal, and we are most praised or blamed for what we intend to accomplish with our work.
But we are responsible for more than just the intended outcomes of our choices. We are also responsible for unintended but readily foreseeable uses of our work. This is in part because we are all responsible for thinking not just about what we intend, but also what else might follow from our chosen course of action. In cases where severe and egregious harms are plausible, we should act in ways that strive to prevent such outcomes. To not think about plausible unintended effects is to be negligent -- and to recognize, but do nothing about, such effects is to be reckless. To be negligent or reckless is to be morally irresponsible, and thus blameworthy. Each of us should think beyond what we intend to do, reflecting carefully on what our course of action could entail, and adjusting our choices accordingly.
It is this area, of unintended but readily foreseeable (and plausible) impacts, that often creates the most difficulty for scientists. Many scientists can become so focused on their work (which is often demanding) and so focused on achieving their intended goals, that they fail to stop and think about other possible implications.
Debates over "dual-use" research exemplify these concerns, where harmful potential uses of research might mean the work should not be pursued, or the full publication of results should be curtailed. When researchers perform gain-of-function research, pushing viruses to become more transmissible or more deadly, it is clear how dangerous such work could be in the wrong hands. In these cases, it is not enough to simply claim that such uses were not intended and that it is someone else's job to ensure that the materials remain secure. We know securing infectious materials can be error-prone (recall events at the CDC and the FDA).
In some areas of research, scientists are already worrying about the unintended possible downsides of their work.
Further, securing viral strains does nothing to secure the knowledge that could allow for reproducing the viral strain (particularly when the methodologies and/or genetic sequences are published after the fact, as was the case for H5N1 and horsepox). It is, in fact, the researcher's moral responsibility to be concerned not just about the biosafety controls in their own labs, but also which projects should be pursued (Will the gain in knowledge be worth the possible downsides?) and which results should be published (Will a result make it easier for a malicious actor to deploy a new bioweapon?).
We have not yet had (to my knowledge) a use of gain-of-function research to harm people. If that does happen, those who actually released the virus on the public will be most blameworthy–-intentions do matter. But the scientists who developed the knowledge deployed by the malicious actors may also be held blameworthy, especially if the malicious use was easy to foresee, even if it was not pleasant to think about.
In some areas of research, scientists are already worrying about the unintended possible downsides of their work. Scientists investigating gene drives have thought beyond the immediate desired benefits of their work (e.g. reducing invasive species populations) and considered the possible spread of gene drives to untargeted populations. Modeling the impacts of such possibilities has led some researchers to pull back from particular deployment possibilities. It is precisely such thinking through both the intended and unintended possible outcomes that is needed for responsible work.
The world has gotten too small, too vulnerable for scientists to act as though they are not responsible for the uses of their work, intended or not. They must seek to ensure that, as the recent AAAS Statement on Scientific Freedom and Responsibility demands, their work is done "in the interest of humanity." This requires thinking beyond one's intentions, potentially drawing on the expertise of others, sometimes from other disciplines, to help explore implications. The need for such thinking does not guarantee good outcomes, but it will ensure that we are doing the best we can, and that is what being morally responsible is all about.