Are there any animal-free/synthetic surfaces that are suited for growing organoids?

Answer

Corning® Matrigel matrix is one of the most successful animal based extracellular matrix that has been used to culture organoids. There are multiple reports on engineering a synthetic matrix to grow organoids with the studies being compared to their morphology/functionality in Matrigel matrix. Researchers have succeeded in generating them for a specific organoid or application and there is a lot of ongoing work. Example can be found in references listed below.

http://www.nature.com/nature/journal/v539/n7630/abs/nature20168.html

http://www.pnas.org/content/113/44/E6831