Translation:I am happy that this law has passed.
Je suis heureuse que cette loi soit passée translates as I am happy that this law has passed. Je suis heureuse que is followed by a subjunctive. The French now basically only use the present subjunctive. And in any case as "je suis heureuse" is a present tense, the sentence would require the present subjunctive. Hope I have answered your question, because in fact I was not really sure what you were asking.
I think I understand Kelly_Laura's point. In English, to describe a law as "passed" is to describe its state. "The law is passed" means that at some point in the past (perhaps the immediate past, and the votes were just counted, or perhaps 100 years ago), it came up for a vote and received the required number of yea votes, which was the act of its passing. So a law that is passed is the same thing as a law that has been passed or was passed.
Because the French sentence is in the present tense (soit passée), one might think that the correct translation also would be in the present tense (is passed -- although, in the subjunctive, it's "the law be passed" -- but we in English would not use the subjunctive unless, for example, it hadn't passed yet, but we were wishing that the law be passed, or we were wondering what life would be like if it were passed last year).
I don't quite follow your previous statement that "je suis heureuse" in the present tense requires the present-tense subjunctive. How would I say "I am happy that the Civil Rights Act was passed in 1964"? (And in English, that past-tense subjunctive would be the law "were passed", although the pluperfect "had been passed" might be more appropriate.)