

The result of either choice – boycotting places that pay less than minimum wage, or not tipping at those places – doesn’t change the fact that the staff are being underpaid, which is the root exploitative practice.
Yes, but boycotting those places is justifiable. Going anyway and just not tipping is actively participating in the exploitation.
No, they cannot. Disagreement here is not reasoned, it is just another example of clever people using their cleverness to justify unreasonable prior beliefs.
You can boycott a business, and write them to express that your boycott is based on their tipping policy. That would be a reasonable strategy to support the workers.
By still giving the business owners money, knowing they pay their staff sub-minimum wages based on the convention of tipping, and then not tipping, you have not communicated any disapproval to management. You have in fact directly supported the business owner exploiting their workers, and joined that exploitation for personal benefit. That’s the opposite of supporting the worker.