This will be site dependant, however in most cases, yes, it should be safe to interact with a site that hasn't fully loaded. Many sites are designed with priority loading where the most important page elements are loaded first and supplemental elements are loaded in the background. The reason the site are designed this way is so that you can start interacting with the main content without having to wait for the less important data to load. Browsers makers spends quite a lot of their time thinking about how to safely load a page incrementally while all the resources are loading in parallel, and the are features in modern HTML for web developers to control this loading.
It is possible for a poorly designed page to break if you interact before it's ready, however in my experience this is very, very rare in practice. Most sites would hide any elements that can break until it's ready, or show a loading interstitial page if the developer deems it necessary, but the occasions where these are necessary are very rare as most things in HTML and CSS are safe to interact before page load finishes.
I believe that this can often cause history corruption,
If you're seeing history corruption, that's definitely not caused by interacting page while it's loading.
however could there be any cases where interacting with the page causes information to be POSTed to the wrong destination, or a hyperlink destination to be incorrect resulting in you accidentally visiting a phishing site, etc?
I can't think of any realistic scenario where you'd accidentally post to a phishing site due to incomplete page load. While it's not impossible, the developer would have to go out of their way to make this a possibility.