Registration by local immigration service is mandatory for foreigners. All fully licensed hotels do it at check-in. Some few hostels have not a hotel status and can't do it and so will refuse foreigners. I had it once, in Susunam, 600km north of Magadan. Many so-called mini-hotels (ie. former kommunalka redone for hostelling) are still in the grey and don't register don't even care, take anyone.
Last october in Sankt Peterburg, in the middle of Vosstanya street, I had the case. Handed my passeport and the girl at reception "what for? You paid you get the room. That's all".
I have stood weeks in a row at rented flats where landlord didn' want to bother.
What i have done always no matter what is get registered at the beginning of my stay. Get a room at some hotel and done. So you are recorded into the system.
Hikes and camping is exactly the case when registration is not possible.
Law has changed over the years. Until early 2010's stamps were put on the back of the immigration card. This was phased out but it took time for it to be known everywhere.
In 2007 i did spend time in Ekaterinburg, Izhevsk and Kazan. Part at a contact, part rental without registration. Had a flight from Kazan. There were passport controls to the gate. The guy who checked my passport had a look at my immigration card and told me there were couple weeks with no stamps. I told him "i was in excursion, forest and lake, cabin". He was ok with that. After, i used to book a hotel room for a night once in a week, just to play safer.
In 20 years, i never had any feedback nor remark nor question when reapplying for a visa.
When i stood with a friend who registered me, because he was curious how it was done, it was in 2006. Did it at post office. Went with him because my passport data. He got the forms and we did seat aside to fill them. He returned to the window to get a stamp then we went to a Sber he had to buy a small cheap administrative briefmark/stamp then back to post office, stamps glued on the form to be sent to OVIR/FMS, and he gave me the duplicated stamped form that was for me.
It has been greatly simplified since.
Excepted first travels i was on multi entries visas one to three years. In this case registration should be done by the inviting organization. In practice it doesn't matter. Just get a hotel room in the first days and done.