What will happen to infrastructure specialists when organizations inevitably shift to the cloud?

They will need to accordingly make the pivot or find something else to maintain.

The cloud does not manage on its own. You still need an infrastructure team to manage and administer it. You still need someone to design it, protect it and troubleshoot it.

I think hybrid cloud will become the new normal in near future. Some workloads just don't work as well in the cloud or the cost just does not justify's it.

I've seen many companies that moved things to the cloud early on are moving some workloads to on-prem (not in their server room where it used to reside originally but to colocation facilities or their own private cloud).
We will see more and more HCI and hybrid-cloud deployment, stretched clusters between multiple on-prem and cloud locations.

Some companies will always keep things on-prem due to various reasons like security, compliance and governance.

The rise of cloud does not decrease the infrastructure positions and opportunities, it does change them and their scope evolves, but we are in technology and that's part of the industry.

The cloud is still infrastructure, just someone else owns the infrastructure. It will mean less jobs is the Infrastructure area but those trouble shooting skills will still be needed. I moved from Infrastructure to Apps, to Control Systems to Networking to Apps …. Keep learning and you always have options

We still have legacy companies—hospitals, manufacturing, etc.—that can't move away from having a physical network. But they’re going to be few and far between in the near future.

I think we have some time before that will occur with platforms as a service like Azure and AWS. The people that I work with today are in Azure or AWS, and it's totally different than on prem. It's a different skill set, but a lot of them are adapting to it. What happens after that, I don't know.