Sorting sequences independent of color

RB = R~Join~B;
NumericalSort[RB]

An alternative, slightly longer, solution could be:

RB = R~Join~B;
order = Ordering[N@RB[[;;,1]]];
RB[[order]]

With the same output as above. This can be convenient when the style of the two lists is different (as in comment below, one might be Bold while the other isn't): slicing the combined list when finding the order (i.e. doing order = Ordering[N@RB[[;;,1]]]; rather than order = Ordering[N@RB];) allows to ignore the differences in style between the two lists and only look at their numerical values.

The issue is not styling, but the fact that the sort order used by Sort does not correspond to numerical ordering here:

Sort[{10 Pi, Pi^2}]          (* Out: {10 π, π^2} *)

You can explicitly sort by numerical value using SortBy:

SortBy[{10 Pi, Pi^2}, N]     (* Out: {π^2, 10 π} *)

So in your case:

SortBy[Join[R, B], N]