Hi! There shouldn’t be any issues except you might find it hard to register for public platforms if you don’t have a government registered business. It can be done (I was able to get a bank account and a stripe account for our private foundation) but it can take a bit of explaining to help the public platforms (like Airbnb) to understand your entity.
And sometimes their policies can change, or it will depend who you speak with in an organisation.
For example, I was able to register a .asn.au domain a couple of years ago, but when my daughter tried 6 months ago, they wouldn’t let her.
There are workarounds if you do hit a roadblock. For example, if they require some kind of government registration to set up an account, go ahead and get the government registration, but when it comes time to renew, just let it lapse.
Hope that helps!