"its really lazy parenting" - opinion, not fact AND unkind
"you are going to be 'that parent' when your child starts school" - opinion, not fact AND unkind
"you will permanently change the shape of her mouth" - use of will not factual, or presented kindly. It may change the shape of a child's mouth, it won't definitely.
If you need a stranger to point out when things haven't been said in a nice way - you've got a problem. The same argument could have been presented much more supportively:
Speaking as a former primary school teacher, I’d gently encourage parents to start thinking about moving away from nappies and dummies by around age 4 where possible. By this stage, most children are developmentally ready for toilet training and reducing dummy use, and doing so can really help them feel more confident as they begin school.
Of course, every child is different, and there are absolutely valid reasons (such as SEN) why some children may need a bit more time and support.
It’s also worth being aware that prolonged dummy use can sometimes impact speech development and the way a child’s teeth and mouth form, which in turn may affect pronunciation and early reading skills. Because of that, gradually phasing it out can be really beneficial in the long term.
If you’re finding it difficult, you’re definitely not alone, as an ex teacher I've got access to a whole host of support resources if you want to message me privately.
As I said, nothing to lose by being nice, particularly with someone who's clearly overwhelmed.