According to English Grammar Online 4U, would can be used in a future tense as a Conditional I Progressive tense.
The conditional I progressive puts emphasis on the course of an action that might take place.
The phrasing might blurs the line, as in your example, September 5, 2015 almost certainly will take place and it is a documented fact that Freddie Mercury was born on that day in 1946. Let us focus on the conditional part of the tense instead. In a broader definition, would can be used in a tense that EnglishPage.com calls Past/Present/Future Unreal Conditional + Continuous.
If-clause: [were + present participle] + Result: [would be + present participle]
Future Unreal Conditional + Continuous can be used like the Future Continuous in imaginary situations to emphasize interruptions or parallel actions in the future.
NOTICE The future form looks the same as the present form. The future is indicated with words such as "tomorrow," "next week" or "in a couple of days."
Breaking this down further, the Future (Real) Continuous tense is what you correctly identify as the will be usage, if he were alive. Unreal modifies this tense to work in the case where Mr. Fahrenheit is deceased (which is the current reality). The two key components to identifying this as the Future Unreal tense are:
- Using a future date. You chose to name the exact date of September 5th, 2015, thus to identify it as a future date we need the additional context of the current date. If you instead started your example with Next year..., this would match the examples from EnglishPage.com exactly.
- The implicit conditional. The phrasing you're mentioning is common enough that a native english speaker will understand that you're referring to a deceased person. Therefore, your sentence ends with an implied ... if he were still alive.
Putting this all together, the correct phrasing for identifying a future birthday for a deceased person is
September 5, 2015 would be Freddie Mercury's 69th birthday.
The form is reversed from the examples above, but it is a valid construction.
Subject (future date) + would be + present participle (birthday) + if clause (implied: if he were still alive).
As Tim points out, though, tenses are loosely enforced in English and many native speakers would correctly parse would have been correctly.