The real question to ask is, are you asking whether Einstein's contributions were important, or was Einstein as an individual important? If the latter, are you asking, would someone else have come up with the same ideas anyway if Einstein hadn't?

Einstein is largely credited as helping to usher in a new period of physics ("modern physics") which includes not only Relativity but Quantum Theory (Einstein is sometimes called one of the fathers of the "Early Quantum Theory" as opposed to Quantum Mechanics which came later and Einstein himself did not like). For scientists this not only meant a new understanding of the universe, but the idea that someone could, largely from pure thought, overturn centuries of previous understanding was a major revelation. Einstein was celebrated not only for his physics but for the idea of someone ushering a new revolution at an unexpectedly late date, and the "Einsteinian revolution" has long been the canonical case study for understanding major scientific change (for better and worse, as it may not be typical).

Did Einstein's ideas lead to the atomic bomb? Not really, or, at least not to the direct degree that many people believe. I have written on this at length, but in short, the path of scientific work that led to the discovery of nuclear fission (and thus nuclear weapons) was somewhat different than the work that Einstein contributed to. E=mc^2 tells you why nuclear reactions don't violate the conservation of energy rule, but it doesn't tell you how to make a bomb or whether one is possible. The physics used to make a nuclear weapon is actually non-relativistic, which is to say, does not use Einstein's equations at all. Einstein's contributions here are heavily over-emphasized, and the reason for that is pretty straightforward: people like the idea that something as powerful as the atomic bomb came from a simple theoretical equation, and Einstein's letter to FDR (which didn't really start the real project, but this is an aside) was used to validate the US government's (later) decision to build an atomic bomb (after all, if Einstein thought it was a good idea, who could argue with that?). Einstein himself used the fame to push his political positions. So everyone benefited from giving Einstein a lot of credit, despite the fact that he was not especially important for that development from either a scientific or political standpoint. Einstein himself did not work on the Manhattan Project (he was excluded for several reasons, including his political beliefs, but also because the kind of physics he did was not really similar to the kind you'd need to make a bomb).

Finally: if Einstein had never been born, would we have had the Einsteinian revolution anyway eventually? It's impossible to know this, of course, but there are many reasons to think the answer is "yes." There were many people working on similar topics in physics as Einstein was working on in 1905, and some were coming very close to the same sorts of answers. It is reasonable to assume that the main aspects of Special Relativity and General Relativity would have been accomplished within a few years of Einstein's efforts. How many years? That's hard to say. But Einstein's work only looks totally discontinuous (i.e., "out of the blue") if you don't know all of the other work being done at the same time, on similar issues. Einstein did make a few daring intellectual leaps, and he did several major accomplishments at once, and that does deserve recognition as highly unusual. But if we assume that Einstein's theories are part of nature itself, then we can safely assume that other smart people would have stumbled across them in time. I would note: you can give this answer for pretty much anyone in the history of science. It is one of the fundamental arguments about science: individuals matter less than our culture likes to believe, when you are talking about collective knowledge production on the scale that one gets by the 20th century. This does not devalue individual work, it just emphasizes that if you have thousands of people studying similar topics, a few of them will eventually hit upon the same answer. We see simultaneous discovery (and invention) too often to presume that it is about "genius" alone.

In short: Did Einstein make a difference? Sure. Was his work important in physics? Definitely. Did he make the atomic bomb? No. If Einstein had never existed, would human history be substantially different? Probably not. All of these are different ways to talk about "importance," which is a tricky concept to apply in history.

To put Einstein's work in context, Helge Kragh's Quantum Generations is an excellent, clear-headed, technically-informed history of physics in the 20th century that avoids biographical exceptionalism in describing the interaction between discoveries, theories, and the context of knowledge production.

Many people don't realize that his Nobel prize wasn't for the theory of relativity but rather for his discovery of the photoelectric effect. In turn, this was a huge piece of evidence in the discovery of quantum mechanics. He also did work contributing to solving the UV catastrophe by expanding on Planck's work and postulating particle wave duality of light. So in those respects, he was integral to the discovery of basically all modern chemistry. Depending on how you want to define "change the world", you might argue things a little differently but I don't think there's any doubt that everything from electronics to modern medicine wouldn't be possible without our current understanding of quantum mechanics, which he was integral in discovering.

His theory of relativity is, of course, very significant, too. Considering how surprisingly often it pops up in science, I think you can make another argument for how he changed the world. On Earth, the theory of relativity is necessary for the understanding and control of particle accelerators and synchrotron sources which are used to advance fundamental science but also a lot of materials science (in particular) and to a lesser degree, bio chemical science. That's based mainly on the usefulness of x-ray sources for small angle scattering experiments which are a large part of what's needed to determine protein structure. In addition, relativity is needed to fully understand and predict heavy elements structure, so you could argue that certain medicines like platinum based anti cancer drugs are at least partially due to Einstein. Finally, relativity is fundamental to rocket science and astrophysics. Most notable to the average person would be the fact that GPS relies on ultra accurate time being kept and I'm reasonably certain that satellites need to take relativity in to account to keep this. So in a way, you can credit Einstein with your GPS working.

While some of these may only be tangentially related to Einstein, I think you'll find that any scientific break through has several unintended areas of application. So the question of how much can directly be attributed to him is unclear, but I think you can safely say that he did contribute to the way the world changed between then and now.

Regarding his role in the creation of the atomic bomb, u/restricteddata has written about this before, both here in an AMA and also on his personal blog, which might be of interest to you.