BA are still notionally a full service carrier. As such they tend to try to work with the customer rather than follow the very prescriptive approach of the low cost carriers.
Low cost carriers like EasyJet, RyanAir, Whizz etc make more money from luggage than they do from the flights so everyone is under instructions to be very strict on luggage dimensions and you *will* get your luggage checked. BA flights are always much more expensive and usually come with a checked baggage allowance as well as a generous cabin baggage allowance, so if something doesn't fit it will generally go in the hold for free and BA make no extra money from it. On the low cost carriers if they can pick you out for this you end up paying airport luggage prices which are a significant extra cost.
The low cost carriers also don't have business class. Whilst notionally business class on BA has the same carry on limits as economy in practice they are very lenient because they do not want to annoy their premium flyers who provide them with a lot of their revenue. And again, there is no incentive for crew to be strict.
The only time your bag will get taken off you and placed in the hold on BA is if you are in economy and the flight is very full. They will often try to get people to put their large cabin bags in the hold in this case because if they don't it can slow up boarding as people struggle to fit things in the overheads. If that happens and they try to tag your bag at the gate but you are in CE or have status, just mention it and they will move on. I have never seen bags taken off people on long haul flights.