When someone is blinkered, they're narrow-minded, or have a limited understanding. Your brother is blinkered by his belief that only boys should belong to his secret club.
The adjective blinkered describes anyone who lacks the ability to include different viewpoints and experiences in their own understanding of the world. Your might think your grandfather wouldn't make a good president because, despite being a nice guy, he's blinkered by his old-fashioned opinions. This figurative meaning comes from the blinkers or "blinders" worn by horses that force them to focus only on the path in front of them.