I have been to Russia too and I think what possibly makes things worse there is just the sheer level of police corruption and beauracracy. For example the police have this scam where they ask you for your passport on the spot, knowing that it is a requirement that every hotel/hostel must hold your passport for 24 hours for a "verification period". If you can't produce the passport, you are hit with a heavy fine. Also be cautious with your camera, as a general rule, never take a photo within any distance of the guards at or especially on the undergrounds, as that is liable to get your camera smashed in front of your face.
I don't think the Russian fans are as outwardly hostile as the Slovaks but you will be continually eyed every time you step onto a metro until the time you leave it. I must have been stopped and searched about 30 times between the metro stop and the grounds of the Luzhniki for contraband, yet the Russian's would spark up flares etc every few minutes. The crowd were pretty racist that day towards Phil Babb, but I gather things have moved on great deal in terms of racism in football since then, as there are now several Brazilians actually playing in the Russian Premier League.
Great trip, so much to see and do, my advice would be just to have your wits about you.