Do front end developers need to know how to use Photoshop?
I'm a front end developer that has never used Photoshop before and always designed my websites in browsers directly. I know that website development has changed a lot since responsive design came into play.
Is Photoshop still used to design websites? Should I invest in learning the tool?
Is Photoshop still used to design websites?
Yes, this is still quite common.
At companies where the team is large enough to have designers and developers separate, PSDs are often given from the design team to the development team. There are often 1-3 versions of a site showing how it will be responsive.
Should I invest in learning the tool?
In my few years of experience working as a front end developer, I've needed to be able to open PSDs and navigate them (open different layers, get color codes, etc.) but never had to edit any given to me. This is because my work is in code, not fixing a PSD. As such, you should be comfortable doing this if you're working at a company that has this type of workflow.
Ultimately it depends on the company you're working at and the workflow that they have. Front end developers aren't generally required to know how to use PS or any other Adobe software intimately.
With that being said, knowing how to use such a tool for asset creation of your own personal projects can definitely be beneficial.