Much depends on the construction. Just to say "fiberglass tubes" says nothing about how the fibres have been oriented, what the fibre/resin content is, etc. Just as you have to choose the right spec of aluminum, you have to choose the right spec of FRP tube.
PJR says that GRP tube is "too flexible unless used in large diameters", which is not at all the same as saying "not strong enough". The spec is not mentioned, and we have to remember that PJR was written in 1988, when pultrusion technology was not well advanced.
The JRA, as an association, cannot and does not voice an opinion on the matter; its members can and do, though.
I have been using GRP battens successfully for many years, and much prefer them to aluminum. If you were in the UK, I would immediately point you towards my current source, but unfortunately I have no direct knowledge of products available in the USA. All I can say for sure is that in Weaverbird's JR sail, the same size as yours, I found 30mm OD x 27mm ID GRP from this supplier to be just a little too flexible for my taste, though they were strong enough; whereas 38mm OD x 34mm ID is amply stiff and strong. I cannot say, though, whether any tubes that you can buy would match up to this performance. You would have to obtain and test a sample tube.