In my experience, this is nothing more than an urban legend at this point. There are great standards, like DMARC, DKIM, SPF, proper reverse DNS and more, that are much more reliable and are actually used by major mail servers. Pick a free service that scans the publicly visible parts of your email server and one that accepts an email that you send to them and generates a report. Make sure all checks are green. After an initial day of two of getting it right, I’ve never had trouble with any provider accepting mail and the ongoing maintenance is very low.
Milage may vary with an unknown domain and large email volumes or suspicious contents, though.
Weird, I’ve never had problems over the past 15 years or so and I’ve been using VPS servers exclusively. Maybe my providers were reputable enough.
I realize my evidence is only anecdotal, but that’s why I started “in my experience”. Also, common blacklists are checked by the services I mentioned.