Not all Russel Group uni's are better than every non-RG uni, my uni was higher ranked than a quite a few RG uni's for my course. (And yes, I had offers from RG uni's, I chose not to go to them)
And despite going to a non-RG uni, I still got a good job, and so my did my course mates, some getting jobs at some of the biggest companies.
So no, going to a non-RG uni isn't going to be a disaster, it's just a weird TSR obsession with them. (And why trust kids who haven't even gone to uni or entered the world of work yet? They just look for reasons to make themselves feel better than others)
I've NEVER seen an employer ask for a RG uni degree, or favour them.