At the end of the day, everyone who is hesitant should speak to a trusted GP about vaccination. With that aside, here's my thoughts.
They've been the most closely scrutinised vaccines in human history. Doctor Norman Swan (who's great on CoronaCast) has a great article about it. Billions of doses have been administered now - if there was an issue, we definitely would've seen it by now. We were able to rapidly develop vaccines for a multitude of reasons. Our own TGA (which is one of the strictest in the world) has a knowledge-base about this.
We're so lucky to live on an island country. Other countries have not fared as well and countries like Germany with as much resources as us are still struggling. We're really lucky that we feel like COVID-19 won't impact us in Australia because our states, by in large, have done the right thing in using a system of resources to minimise spread and impact until vaccines arrived. Without it, we'd have a lot more deaths (see above) and worse, a lot more people with long-covid, which sounds awful.
Every side-effect, every death post vaccination, every reported sniffle is logged and checked. That data is also widely available - nothing is being hidden. This data has been misreported by politicians and fringe circles en masse, circumnavigating our spam and privacy acts in the process. More often than not, opposing, conservative opinions cherry-pick data or publish data in journals that aren't well known and aren't subject to peer review.
Our federal government wasn't bothered to build quarantine facilities that it was supposed to by law, it refused to roll-out a national strategy for COVID-19 until it was forced to and absolutely bungled/lied about getting vaccines when we needed it. During that time, they spent millions on an app that didn't use global standards and was essentially a massive failure. And when our states stepped in and did all the leg work, not only did Scott Morrison take credit for it, but when conservative voices rioted and suggested violence against our states, he side-stepped condemning what is absolutely, without a shadow of a doubt, abhorrent behaviour.
Our federal government couldn't pour water out of a boot if the instructions were on the heel, let alone coerce and force people into getting vaccinated.