In Australia, the hiring and recruitment for government departments is going to be different to a software company, start-up or somewhere more commercial - so that is very relevant to your question. The difference you will normally find is high-volume, low-skilled HR / recruitment admins doing screening for government while hopefully more experienced recruiters for the other jobs.
I like seeing personal and side projects on CVs, while I'm not an engineer, I highlight these projects to our engineers who review tech abilities and can dig in. I think that entrepreneurial spirit, motivation and self-taught skills and personal interest projects with new technologies (what a lot of people use github for) are a lot more desirable in the private sector...
In most cases, you would find the government recruitment process to be a lot more automated, e.g. using a CV parsing database, looking for key words and taking a 'check box' approach to screening. I doubt whether 8/10 government recruiters for programming roles know what github is.
To provide direction on how to make the best of it (besides applying for private sector jobs), I would recommend that you clearly list your relevant github projects - but would classify them in a section below your employment experience. Make sure to use examples that clearly link to the required skillset - and assume the assessor is not a programmer... so make sure you have a quick summary which would describe what technology / tools you used so a lay person can understand why it is relevant.
If you have a section of technical skills, such as a matrix or tech summary, I would include the skills you learnt via github projects, but be sure to be honest and upfront throughout the whole interview process about where you learned and used those skills.
I personally find it a bit annoying / deceptive when people are purposefully vague about experience - whether that is not specifying volunteer vs professional work, dates, location, enhanced job titles, part-time vs full time, or exaggerating their experience, etc.