I’ve often come across articles saying we should not start a sentence with a conjunction. However, many many times have I seen a sentence starting with ‘But’. Isn’t But a conjunction? Or is it an exception? I’m very confused about what actually is the rule here. Please explain.
But of course you can! It's quite common. It's not a hard rule, it's just a recommendation found in some (not all!) style guides for formal and professional writing. In everyday language it's perfectly normal and acceptable to begin a sentence with a conjunction.
Another commonly cited "rule" is to avoid ending a sentence with a preposition. This is also only a recommendation and nowadays almost always disregarded. This led to a famous quote, often wrongly attributed to Winston Churchill:
This is the type of arrant pedantry up with which I will not put!
In general, it sounds weird to begin a sentence with "but", except in the British idiom "but of course".
In cases where you would want to use "but" at the beginning of a sentence, "however" is usually a suitable replacement. For example, in your comment on TypeIA's answer, I would have said "I'm a newbie so I can't upvote. However, I'll accept it".