Does U.S. constitution allow for discrimination of foreign born citizens pertaining...

[Sir Famous]

...to becoming a President? Does U.S. constitution allow for discrimination of foreign born citizens pertaining to becoming a U.S. President based on country of origin the same way others view homosexuals? Because one side we have denial of opportunity based on national origin and on other side we have denial based on sexual orientation. We could argue since constitution denies opportunity based on national origin and previous law denied opportunity based on sexual orientation. Since Homosexual are trying to achieve equal opportunities, should foreign born fight for equal change to become a President? Or should we continue to deny the citizens of United States willing to run for the office but unable based on their previous nationality the same way we used to deny opportunities to homosexuals based on sexuality?
So, since foreign born are being denied the opportunity for equal rights. Should homosexuals be denied the same rights as well?
Also, note that discrimination irregardless of circumstances HURTS. So shouldn't it be viewed as equal to that of homosexuality issue that is swiping the nation for absurd reasons? Or should we just do away with both issues which although different have the same outcome. The outcome is ousting or hurting the minority. Why should a homosexual minority be any different than foreign born citizen minority, ignore the fact that America is where it is today all because of immigrants.