Not only that, but a lack of Nazi ideology would affect the motivation of German soldiers to fight. Probably not enough to make them not fight, but still enough that they’d be less tenacious in fighting. Even the most militant of non-Nazi Germans were incredibly wary of actually starting a war with the rest of Europe. If you go around invading other people with little to no provocation, you need to give your own people a very good reason as to why your people deserve other people's stuff more than they do themselves, and racism is very good at providing that reason.
This isn't just talk. People need a reason to lay down their lives for their country, and states that are unable to provide sufficient reason often fold under pressure. Fascist Italy is a good example. Although Italy certainly had some of the same racist dogma, it wasn't as pervasive or as popular. Once the going got tough, the Italians asked themselves just what the hell they were dying for, then threw in the towel. A country doesn't fight to the bitter end for nebulous reasons. The Germans fought incredibly hard in WWII because they had a pervasive ideology that made sense to them. That ideology told them they were better than everyone else, deserved to be on top, and were justified in killing anyone else until that became a reality. It was incredibly evil
and racist, but as a motivational tool... it worked.
Without Hitler and his madness - of which racism was a big part - flogging them on, odds are good they pull back from the brink when the Anglo-French finally put their foot down in Poland. If they DO end up in a war they fight it with much less energy, all while looking for an early negotiated exit, allowing them very modest territorial gains... or at least avoiding total losses.