This is a subject that is fraught with anxiety for many families!
When I see a family for the first time with a small child who is not talking well, parents are often surprised when I ask questions about feeding and eating. I ask about early feeding (Was the baby breastfed? Were their any difficulties latching on? How easy was it to transition to solids? What about eating lumps?)
Some children are fussy because they don’t like certain flavours, or just “like what they like”. Some children are allowed to develop fussy tendencies. But most of the children I see that eat a limited range of foods do so because it is actually hard for them to manage various textures. It can be particularly hard to manage meat and food that has mixed textures.
Children with dyspraxia have difficulty planning how to use the muscles of their mouth, lips, tongue and palate. The other muscles needed for swallowing can also be involved, including around the pharynx (at the back of the mouth, above the entry to the osophagus).

Fussy eating can be a symptom.
Not all children with dyspraxia are affected orally like this, but many are. A Speech Pathologist, as well as helping with speech, can help you to introduce and modify other textures.
Sometimes this can be done by taking a flavour your child particularly likes and presenting it with gradually modified texture over time. For example, if a child will only eat apple when it is pureed, but enjoys the flavour, puree it less and less over a few weeks.
If you have experience of a fussy eater, please leave a comment. Let us know if you have found strategies that work!