Have you read Southgate's statement made only yesterday - it gives you a very clear understanding of what he believes in (you state that you have no idea what he believes in)?
He makes his position very clear what he and (if we are being pedantic) what he believes the players think about this. Jordan Henderson, a senior player has also very recently confirmed that the squad is united with Southgate on this. Southgate has made several statements about racism in the past and these have always been consistent. In short, there is not one shred of evidence that Southgate thinks that it is 'crap' as you would have it, and in fact there is a lot of evidence to the contrary. So we do know a lot about what Southgate and the squad think.
Did you read the link about cognitive dissonance? What you are suggesting is a fantasy interpretation of the available evidence, but one that I think would confirm your underlying belief. It is very uncharacteristic of you to argue from a position where there is not one iota of supporting evidence, but needs must.
I have already answered your question (i.e. there is no evidence) but I'll go further. If Southgate didn't believe in this cause he would just keep quiet about it, like every other previous England manager. That he is prepared to talk openly about it is a good thing. Fairly naked racism and racist behaviour have dogged the England football team for the whole of my life. Anyone who has attended England football matches will know that it has been a historical problem. Southgate is a part of a solution to some of these problems and is doing something to create a better future for English football. I think he should be applauded for it, it would be much easier for him to remain silent. It creates a problem for all of us (and I include myself) because it forces us to examine our own attitudes and behaviours. And that is why we see so much controversy and distraction about something which, in truth, is a harmless but well meaning ten second gesture.