What? That's not my experience at all; from my desktop, tablet, and/or mobile phone browser I can access all subreddits I'm interested in without having to be logged in, including the one you mentioned, /r/programming but also all of these:
android, askhistorians, biochemistry, c_programming, chemistry, compsci, design, embedded, freebsd, golang, haskell, java, javascript, linguistics, linux, math, mechanical_gifs, openbsd, physics, python, raspberry_pi, rust, statistics, sysadmin, vim, web_design ... and many more.
so not sure what you're doing to not be able to access said subreddit while being logged out.
