Can open science project be performed/published by non-scientists?

Yes, of course anyone can publish an open science project. As many of us in the scientific community wish would happen, the project should be judged on merit, not who initiated it, where they studied, or what their background or education is.

These principles are enshrined in the San Francisco Declaration on Research Assessment (DORA), which have been widely circulated and many (unfortunately not a majority, yet) organisations quick to sign up to.

Yes.

I'm not a scientist. However, let's say that for a project I do research on the genome of a fruit fly. I upload my data to GenBank, submit my pre-print to arXiv, and make sure that my pre-print, data, and overall project satisfy the criteria for an open science project, as given in What criteria does a research project need to match to be called open science?.

While I am not a scientist, I have still performed open science.

No specific training or credential is required to make a meaningful intellectual or technical contribution to an open science project. Training, credentials, where/how research outputs are published, how much those outputs get cited, and so on are primarily concerns of career economics—that is, how does one get, keep, and advance in a scientific career. For those interested in a scientific career, these considerations are important. But ideally there should be nothing stopping someone without scientific career aspirations from contributing to an open science project.