Do you think using Bootstrap and other CSS frameworks would make a developer look less competent?
Yes, if you also tell others that it's the only way you know how to create a responsive layout, or if you claim that you love them and you use them as your primary tool.
No, if you tell others that you primarily code responsive layouts without them, but you can handle them if someone requires you work with them.
With Grid Layout and Flexbox support out of the box in CSS, do you think a developer shouldn't rely on frameworks anymore? What are your thoughts on this?
To me, it's FAR easier and quicker for me to code manually using CSS Flexbox and Grid than using CSS frameworks. I can work with CSS frameworks, but the time and effort I need to spend overriding and customizing their defaults nullify the time saved using pre-defined components.