Then this will be against constitution! No way!

If the constitution says this guy is a citizen, yet the government declines to issues passport for the reasons you cites, it is definitely against constitions, and Supreme Count will definitely say this is against constitution and forfeit the regulation. If such blatent violation of constition is allowed, the foundation of this country will be gone.
I think the only way to get rid of by-birth citizenship is to amend the constitution. It is possible though, since constitution has been amended quite several times now.