The genuine version of the problem
Sometimes two audiences really are irreconcilable: a prospect who has never heard of you and a customer trying to log in, or two sectors that buy for entirely different reasons. Pretending one doesn’t exist produces a page that irritates half its traffic.
First, check they’re really different
Often the two audiences want the same thing described in different vocabulary, which is a copy problem rather than a structural one. Splitting the page in that case doubles the maintenance and halves the clarity for no gain.
Rank them, don’t balance them
Where they are genuinely different, decide which one the homepage is for — usually the audience that doesn’t know you yet, since the other can navigate. A page that serves both equally serves the new visitor badly, and a second call to action divides the first rather than adding to it.
Existing customers can find the login. A stranger cannot find your point.
Give the second audience a door, not half the page
A clear, small, permanent entry point — a nav item, a footer link, a distinct button — serves returning users perfectly well. They are looking for it and will find it; they do not need the hero.
Segment below the fold, if at all
Where two buyer types genuinely need different arguments, make one clear promise at the top and branch underneath into paths for each. That keeps the positioning your navigation is already carrying coherent while letting each audience self-select.
The honest failure mode
A homepage split down the middle into two equal halves reads as a company that hasn’t decided what it is. If the argument cannot be resolved, that is usually a positioning problem being escalated to the design team, and no layout resolves it.