As for how to leave one’s former shul, I think some official (written?) notice is appropriate. The notice need not specify reasons for leaving and should be in civil language.
Consider that shul membership often includes paying membership dues which continues to accrue on the still-active accounts. Shuls often depend heavily on membership dues to fund annual expenses, so the sudden revelation months later that expected revenue will not be paid can be very painful and easily avoided.
Yes, there will probably be an uncomfortable follow-up call from a board member and/or the rav trying not to lose a long-term congregant. I just think it’s the right way to handle such change.