The t-henselian approximation conjecture for algebraic curves

Let $C$ be an algebraic curve over a field $K$, and let $\tau_1$ and $\tau_2$ be independent field topologies on $K$. Two topologies on a set are independent if every nonempty open set for one intersects every nonempty open set for the other.

T-henselian approximation conjecture. If $\tau_1$ is t-henselian, then $\tau_1$ and $\tau_2$ induce independent topologies on $C(K)$.

This is proposed as a technical hybrid needed to adapt arguments relating the Shelah and generalized henselianity conjectures. The source explicitly says that it has not been proved and may be within reach of current techniques.