That's ridiculous. Let's look at Jan 1958, for example and compare to the 1921-1950 climatology vs. the 1991-2020 climatology. Sure there are some differences with the anomalies being tempered back a bit, but we're not looking at drastic changes which make older analogs obsolete. They absolutely are still relevant.
EDIT: some differences may also exist here as I am using two different data sets but this is because NCEP/NCAR only goes back to 1948 so to make 1921-1950 climatology I had to use 20CRv3.