Yes: A lot of web-development has already been automated for simple sites. Think of how many more web-development jobs would need to exist if Wordpress and Squarespace and other CMS systems weren't powering so many blogs and simple crud apps.
No: Unlike other workers who face being automated out of a job, web-developers are the people doing the automating. Wordpress and Squarespace are being built by developers, after all. In order for my job to no-longer exist, some other engineer has to come in and build something that replaces me. So if you want to be future-proof, all you need to do is make sure you're the developer doing the automating, instead of the developer being automated.
In short: it's dog eat dog. Keep eating other dogs and you'll be fine.