I've seen some DMs allow characters to call this on a case-by-case basis. But in my experience, allowing the blocking characters to say "I'm going to choose to allow/deny this movement through my space" leads to some fairly messy adjudication, and can result in the normal movement rules becoming reversed, as characters choose to allow enemies to be shoved through their space into danger, and block their allies from being moved involuntarily. Aside from being awkward to rule on, this tends to devalue forced movement effects.
It's both simpler and a lot more consistent to stick to the normal rules - creatures can move through their allies' space if they don't stop there, but can't move through enemies' spaces unless there's a significant size difference.