Good question. As someone somewhat new to testing, I find it interesting that there are some divisions here. There is a concept of “shift left” (moving testing further up the dev cycle) and “shift right” (importance of post production testing).

Each of us may find a sweet spot for our area of preference but in general I have always taken the approach of continual learning and expanding skillset rather than having a rigid view of what has always been done. So manual testers learning about automation and vice versa. Testers starting to learn about new tools and capabilities to test during development and post production testing like load/performance testing. Having a broader understanding of the entire cycle and process will make us all better in the long run.

This doesn’t necessarily mean that testers should become developers- unless they feel drawn to learn development But building strong relationships between testers and developers is never a bad thing.

So short answer… yes, imo.

I think this depends on so many factors with both the individual and company. Some things to consider  for this:

• The tester’s background & existing skillset
• The tester’s current and future position and skillset wishes
• The company size & setup (a one-person startup or a place with established, existing devops teams)
• The company future setup wishes
• Methodologies and working practices used (agile in which everyone should do every role, or where high experience & knowledge is more hightly valued for each specific position) 

I don’t know if there is a one-size-fits-all answer here. My own opinion is they shouldn’t need to, but ideally there would be some opportunities if testers wish to get more involved.