First of all, indeed Vy is independent of wind, as it is defines via pure vertical speed, which is not influenced by horizontal wind.
Vx is defined via the tangent to the climb polar at maximum power. If you movethat polar horizontally (by adding a wind speed to the ground speed), the tangent touches at a different point, corresponding to a diffenent IAS.
In Headwind, Vx reduces, in tailwind it increases. So the change of Vx as GS is even larger than as IAS. Small changes (per definition of the tangent...) do not change much.
gliders do use polar charts or glide computers on the vario/vsi to obtain the best wind penetration glide speed to cover the greatest distance in the shortest time with least loss of altitude or another way the optimum flight path
Actually glider pilots do both. In a competition, speed matters, so you optimize your glide speedwise, not distance wise. You prefer to spend times in updrafts (typically thermals) than in glide, so better arrive a little lower but significantly earlier in the next thermal, as long as it is strong enough to gain more altitude in the longer climb, than you have lost in the faster glide. You basically look at your speed polar from the viewpoint of your compettitor in the thermal ahead. He will see you descending faster, hence you must fly faster to see an optimum glide from his perspective. However, if you do no longer expect to reach your destination, there are no more points to earn for speed, just for distance, you better switch tactics and go for maximum distance.
In practical terms, if Vx matters, you have a mjor obstacle ahead, otherwise you will anyway fly Vy. If you have an obstacle ahead (let´s say a mountain), the horizontal wind will also have a vertical influence, hence your Vx is anyway invalid. Trying to climb over a mountain in strong headwind is no smart idea...