This is one of those times where some nuance is warranted.
The new variation is indeed "more contagious"... at least when compared to other variations. It has gone from being the cause of 30% of UK Covid cases to 70% in the past some-number of weeks. Thus, it's more successful than competing strains. That's how natural selection works.
What isn't yet known - and will not be known for perhaps several weeks, if ever - is whether it's causing the disease to become more contagious, and if so, by how much. Since there are so many factors behind the reproductive rate (Rt or R0), any subtle differences may get lost in the noise.
Here is the CDC's current guidance:
CDC provides credible COVID-19 health information to the U.S.
www.cdc.gov
Until there is significant herd immunity (through infection or vaccination), it is unlikely that the virus will mutate in such a way that evades the immune system - there is not yet any reproductive pressure to do so. Once we've got some level of herd immunity, then this is likely to happen - just as it does with various cold and flu viruses. It's also not guaranteed to happen - measles so far has not mutated in this fashion. Or whomever is in charge of designing and releasing this agent will make the appropriate changes in order to generate further chaos.
So for now, it's a waiting game, and I don't see any reason for panic. But we're going to get panic whether it's warranted or not.