From my train research, it appears there a two ways to go. First RER to Basel, and then SBB to Grindelwald. The other way is to take local transport across the river in Strasbourg to Kehl Germany, and the DB to Basel and SBB to Grindelwald. The route through Germany is much cheaper without the half fare card. I should there any reason I should not take the German routing?
Are you looking at advance purchase nonrefundable tickets? Then, yes, it would be cheaper, I guess because of ticketing agreement Deutsche Bahn has with SBB. I see you can get a Sparpreis Europa Ticket for 29.90 EUR. Add about 5 Euro for the train from Strasbourg to Kehl (you do not have to get off the train) then trains to Offenburg, Basel, Interlaken and Grindelwald.
That's a new one on me, but yes, it would save you money.
The disadvantage is it would take longer that way.
You can reach Kehl station by Strassbourg tram. If your starting point is not near Strasbourg station, tram may be easier.
ICE Trains from Germany stop at both Basel stations: Basel Badischer Bahnhof and Basel SBB. The onward train for Interlaken and Grindelwald leaves from Basel SBB, make sure you get off at the correct one.
BTW, the French train from Strasbourg to Basel is a TER (Transport express régional), not RER.