FYI I discovered a workaround: if I add the xlabel to the 2nd subplot AFTER plotting the title to the 3rd subplot, the error does not occur:
thing1 = (1:10)';
thing2 = (1:10)';
figure
h = tiledlayout(1,3,'tilespacing','tight','padding','tight');
nexttile
stackedplot([thing1,thing2]);
ax2 = nexttile;
plot(thing1);
nexttile
stackedplot([thing1,thing2]);
title('test 3')
xlabel(ax2,'x')