Should I give my affiliation as "independent" to protest my institution's funding policies?
I'm not sure that I see an ethical issue here.  Ethically, I think you are free to omit your affiliation if you so choose.

But I don't see any benefit to you by doing so.  It may be a symbolic jab at your institution for not funding you, but it's not going to directly hurt them in any way: nobody is going to notice except you and them. On the other hand, it certainly can directly hurt you and your relationship with your institution.  As just one example, they might decline to consider that publication as part of your research record when they evaluate you (e.g. for tenure).  Or, more seriously, they might decide that if you don't want to be associated with them, they don't want to be associated with you; and therefore stop employing you (if your contract permits it).

Clearly you have some issues with your employer, and I hope you are able to improve matters somehow.  But what you suggest seems at best ineffective and at worst self-destructive.