Next week on Friday the 6th, my family of four needs to travel from Munich to Oberammergau for that evening's Passion Play. Will we have any problems using our Rail Pass to get Oberammergau that morning? Do I need to make a reservation?
The trains from Munich to Oberammergau are all regional trains. There are no reservations on regional trains.
If you possibly have any other use for a day of your rail pass, don't waste it on Munich to Oberammergau. All four of you can travel from Munich to Oberammergau, in 2nd class, leaving after 9 AM, for €28 (total, €7 per person) with a Bayern-Ticket. That would also include the trip back to Munich if you do it that night, and any transportation in Munich.
Rather than the link provided by Steve, use this one. It goes directly to the Bahn Query page, where you have more options than on Bahn.com. Put in Muenchen Hbf and Post/Bahnhof Oberammergau. You'll find that they will show only the fastest connection, which about half the time is from Munich to Oberau by train with a bus (included with the Bayern-Ticket, not included with a rail pass) to Oberammergau. However, you can always change at Murnau to a local train to Oberammergau.
The train from Murnau to Oberammergau runs hourly, with 10 minutes to catch it from the Munich train, except for the 1230 train out of Munich. In that case the Oberammergau train leaves a little earlier, before the Munich train arrives, so you'll have to wait an hour in Murnau for the next one.
BTW, if you happen to want to catch the 8:32 train out of Munich, it stops in Tutzing and leaves at 9:01, so the Bayern-Ticket is valid from Tutzing. An MVV Gesamtnetz Partner Tageskarte (day ticket for up to 5 people), for €18,80 will cover you to Tutzing.