Product liability suits against Snap, Inc. and an online gun marketplace demonstrate how courts are increasingly finding less federal immunity for website operators and app makers when serious injuries and safety threats are alleged.

Two state appeals courts recently let claims proceed against the company that runs the popular social media app Snapchat, and gun classified-ad site Armslist, LLC.

While a federal district court recently knocked down a product liability case against dating-app maker Grindr LLC on immunity grounds, the case is on appeal and some legal observers say the trend might be turning to allow more suits like these....