For what it's worth:
On my strawberry marble cake, I substitute seedless strawberry jam for some of the butter and milk in the frosting, and imitation strawberry extract for the vanilla, and add a couple drops of red food coloring (just the ordinary McCormick stuff, from the grocer), to get the pale pink overall coat, and add a bunch more strawberry jam, and more strawberry extract and red food coloring, to get a deep pink with which to pipe strawberry shapes onto the cake.
It's not flavorless, but it's certainly not unpleasant-tasting.
From my strawberry marble cake recipe:
1 lb powdered sugar
1/4 cup butter
milk, as needed
1/4 cup + 1/4 cup seedless strawberry jam
1/4 tsp + 1/4 tsp imitation strawberry extract
red and green food coloring
Combine sugar, butter, and first portions of jam and strawberry extract, and enough milk to make it spreadable, adding 1-2 drops of red food coloring. Once cake is frosted, reserve a small portion, and tint green, for stems. To the remaining frosting, add the remaining jam and strawberry extract, and 2-4 more drops of red food coloring, and pipe strawberry shapes on the cake.
In terms of what I actually do, I have been pulling out the "stem" and "strawberry shape" portions before thinning the main frosting to spreadable consistency, in order to keep them at a stiffer, "barely pipeable" consistency, to reduce slumping.