There's various options depending on your problem. You could just hold firmly onto memory, preallocating all your buffers before the program starts and then don't allow them to be GC'd, you could also use stack allocated arrays like in StrideArrays.jl / StaticArrays.jl, or some combination of the above. You could also just manually use ccall to malloc and free memory as needed I guess.
There's a nice talk here [1] about using julia in soft-real-time for robotics.
I'd say the biggest impediment to real-time programming in julia currently is not the GC, but instead that the language has lots of optional optimizations that the compiler can choose to not perform if it thinks it'd be beneficial to do so, and those optimizations can change between minor versions. Hence, there's a lot of testing you'd need to do to make sure your code really is doing exactly what you want and you won't hit the GC or dynamic dispatch, and you'll need to redo that testing every time you update julia or any packages, which is obviously not ideal.
Essentially most GCs require you to pay for it even if you don't use it in critical sections. I'm not sure if Julia has the semantics for explicitly disabling GC during hot loops, but it is extremely difficult to do that without the dedicate hooks.
The issue is not performance - GCs are usually faster than not. It's determinism.
