Flaja,
You do make good points about the history of Americans of German descent.
First, it seems to me that the USA's involvement in the Franco-Prussian War TTL is a result of Grant's looking for a war. From prior discussions with Robert about the state of TTL US politics in Reconstruction it's not too hard for me to believe that Grant's coalition -- whether he's a Republican or a Unionist -- is very prone to fragmentation. Furthermore, the nation is still putting its own identity to rights after the Civil War. Hence, Grant probably makes use of all the lovely rhetoric of "The Debt We Owe to Lafayette," but's it's not the reason for the war.
Second, it seems to me that the political reasons given above are going to trump ethnic sentiment, particularly in an America where "Northern" v. "Southern" and "Radical" v. "Copperhead" v. "Unionist" are going to be far more decisive political factors. Rather the evidence you supply suggests to me that Grant's efforts to fight the war as a political exercise may be complicated by ethinc sentiment. Even then, I have a hard time seeing the expression of such sentiment acheiving enough clout to prevent the war if Grant's determined on having one (protest the hell out of it, yes).
Third, ethnic sentiment is very hard to track in American politics. It tends to affect local politics a lot by determing neighborhoods and establishing basic us v. them sentiments. This is what I mean when I say I doubt your contention that the "Germanness" of the politicians you list will lead to a united political movement against the war, led by pro-German sentiment. Instead, it may turn the sentiments of groups within whatever coalitions currently animate national elections. I think a lot therefore depends on Grant's political party. If at the time of Grant's election in 1868, the Republican Party is still running as the Unionist party. Given my vague feeling that you'd be most likely to find the most recent German Americans in the Radical wing of the Republican party, due to their usual anti-slavery sentiments, such sentiment may play a role in leading to the fragmenting of that coalition into two blocs, Unionists and Radicals. And even then the primary divide is probably feelings about Reconstruction. This in turn may further influence the fighting and politics of the war by forcing Grant to turn to more moderate Northerners and even Southerners to support the war, the latter motivated by a desire to return to power after the rebellion and to forge a legacy to overcome the "Bloody Shirt" of the Radicals' call for massive social change as a part of Reconstruction.
Anyway, good points all round. Cheers.