Strictly speaking, glass (in the purest form, silicon dioxide, or fused silica/fused quartz) does dissolve very slightly in water. But the amount of silica dissolved into the water is so small that you don't care.
There are certain plastics (relatively expensive) which do not leach. They are used for water storage and piping in the semiconductor manufacturing industry (where you really really want pure water).
There are certain plastics (relatively expensive) which do not leach. They are used for water storage and piping in the semiconductor manufacturing industry (where you really really want pure water).