You don’t need a mashgiach to answer this.
Mixing different types of meat, or meat and poultry, is perfectly fine.
Milk and meat: Not good.
Meat (or poultry) and fish: also Not good, but different than meat and milk.
There are some people who have a minhag passed down in their families not to eat fish and dairy together. An interesting custom that the more learned members of the CR can tell you a lot about. (Some are of the opinion that it’s based partially on a typo. Others disagree.) It makes the classic lox and cream cheese a no-no. Most of us don’t need to worry about it.
By the way, Who was this “someone” in your shul? I’d avoid going to him for advice on Halachic matters.