More accurately, a Rabbi can tell you whom not to marry (i.e., Kohen who wants to marry a divorcee).
I do not believe that Rabbi Schachter said that if a Rabbi knew the parties well, his opinion that they should marry each other would be Halachically binding.
Even Yitzchak Avinu (a Navi) couldn’t impose his wishes upon Yaakov Avinu – marrying the daughter of Lavan was a suggestion, not a command.
Likewise, choice of career can be governed by Halachic considerations. Again, this is usually in the negative (Halacha can disallow certain occupations in some circumstances). I am not aware of any circumstance where Halacha would mandate an individual assume a particular career.
Whom to vote for presumably follows the pattern.