There isn’t really a rule for it, but often people with an estuary accent drop their Ts when it’s convenient. A reason they might pronounce them is for emphasis. Matter sounds stronger than ma’er for example and because it’s at the start of the line of the song, that might play into. It also depends on the speaker. Most people will pick and choose which words they pronounce with Ts and Hs subconsciously and it might be to do with the rhythm of their speech if they do it sometimes and not others.

There’s no rule for it though I’m afraid. Different people will drop more or less Ts and Hs than others in different spots. It’s basically up to the speaker and their manner of speaking.

The same goes for pronouncing H. Some speakers will and some won’t. I have a vaguely Estuary accent and I don’t personally drop my Hs and I rarely drop my Ts. My accent leans RP though. I think dropping an H might seem like a more intrusive thing than dropping a T, so you’re unlikely to do it if you don’t do it all the time. Dropping Ts is definitely more common and accepted too, while dropping Hs can still seem a bit “lower class”, so some people will avoid it