Create a public repo using a new GitHub/BitBucket account for just this task
I'm not sure whether this is normal in the industry.
There is no standardized practise for this as such in the industry. It could differ between companies and people involved.
I'm pretty concerned about about my current employer viewing it.
Your concern is not uncalled for as you may not want a certain piece of code to be associated with you.
On the other hand, should I consider this as a red flag?
I feel you need not overthink it. Possibly the hiring manager or the recruiter isn't as much aware of source code sharing practises and even how source code hosting websites work.
Alternatively, one could reason that it may be easier to share your test assignment between different people/teams for review if it's in a publicly accessible repository.
Again, as you are concerned about having the repository associated with you publicly, you can create a separate GitHub/BitBucket account just for the sake of this task, make a public repo and share the link with the concerned.
Just make sure to disassociate your email address or any personally identifiable information from the commits, GitHub/BitBucket username and conceal any email address from the public profile. This would keep anyone else viewing the repository from associating it with you, while you can also, at any point of time, prove the ownership of the repository as desired by the interviewer.
I don't see any reason to consider it as a red-flag at this point.