The road to success is paved with naysayers and haters. Haters are gonna hate.
Often the best option is unpalatable, difficult and will provoke the naysayers. That won’t work because … We tried that 10 years ago and it didn’t work. I’m not willing to change anything about me even if it might help solve this problem. Criticism is part of leadership. Even if you don’t hear it, you need to be aware that it is out there stirring the pot. When you do hear it, listen intently, measure it against your goals, adapt if the critic has a valid point, ignore if they are pushing their own narrow agenda.
Some criticism will be valid and important. You/we are not infallible but by putting an idea or solution out there, it opens dialogue that would never have happened. Some critics are ill informed (I am misinformed often) and just need more information. Some naysayers are afraid of change and how it will impact them. Some have a small self centered motivation and they will likely be the most vocal and least flexible. All resistance can devolve into ad hominum arguments but the people with the greatest personal stake in obstructing change usually get to the personal attacks quickest.
If you have tested your conscience and are confidant in your motives, hold your ground. Listen for yes/and comments and build your change with those folks.