Facebook and Twitter both used to have RSS feeds, and stopped supporting RSS to force people to use their ad-heavy client interfaces. But that's not where the good stuff is. While "social" has dropped RSS, it's still doing great for real news.
I wrote a simple Twitter API to RSS script and have been using that to read Twitter (via Feedly) for a few years now. The downside is that you don't get tweets at anything even approaching real time (Feedly seems to hit my RSS once every 6 hours), but I find it just perfect for low volume Twitter feeds (like bands announcing new releases or shows).
There is still the option to make your own client or just buy something like Tweetbot which has no ads.
But I hear you. I find Twitter unusable without 3rd party client, and I think that is affecting my experience in an indirect way as well. I think the fact most people see ML picked tweets has caused fewer people responding to what I share now versus 4 years back.
Don't forget to just ask! I usually include a minimal RSS feed example in the email along with some bare basics explaintion. Works surprisingly well. Webmasters care?!
If it puts out content on a regular basis, chances are you can subscribe to it via RSS.