$\newcommand\de\delta$Indeed, a counterexample is as follows: $a=2$, $b=1$,
$$X\sim\frac12(\de_0+\de_2),\quad Y\sim\frac12(\de_0+\de_1),$$
where $\de_x$ is the Dirac measure supported on the singleton set $\{x\}$. 

Then $X\succcurlyeq_{st}Y$, but
$$a X + b Y \not\succcurlyeq_{st} a Y + b X,$$
because $P(aX+bY\ge 2)=\frac12\not\ge\frac34=P(aY+bX\ge 2)$. 

(Your smoothness condition is inessential, since any distribution can be appropriately approximated by a smooth distribution.)