  It has been known since their birth in Bao and Wang's work that the
$\imath$canonical bases of $\imath$quantum groups are not stable in general. In
the author's previous work, the stability of $\imath$canonical bases of certain
quasi-split types turned out to be closely related to the theory of
$\imath$crystals. In this paper, we prove the stability of $\imath$canonical
bases of irreducible finite type of real rank $1$, for which the theory of
$\imath$crystals has not been developed, by means of global and local crystal
bases.
