Grease can be nearly as opinionated as motor and gear oil, no offense taken.
If you have expensive equipment and high quality sealed connectors with the gold plating, I could understand better field experiences without grease.
Then there's the rest of the world with cheap connectors that may not meet spec and have quality issues, where grease often helps.
Some big dont's I've seen:
1) Don't use silicone grease near arcing contacts, like in many switches. Dielectric grease is usually silicone.
2) Don't try to use conductive grease with graphite or metal particles thinking it will make a better electrical connection.The conductive particles can instead cause tracking and damage in a multipin connector.
3) Too much grease can be just as bad as none, especially on connectors regularly plugged and unplugged if it attracts and retains dirt in the connection.
A little dab will do ya.
This is one company with good products for a variety of connectors and equipment in different operating conditions I would trust that had good advice the last I looked, which has been awhile:
Nye Lubricants
Electrical Components