The only time either of my children ever wore a tee-shirt with a slogan relating to either 'mummy' or 'daddy' was when my DS (12) was maybe 5 or 6 and there were a few hiccups with my ex trying to convince our son that he had to call my ex's new wife "Mummy" (DS was horribly confused and panicked for a while that if he had "a new Mummy", what was I to him?!). And so, I had a tee-shirt made which had the slogan, in big, bold, stand out letters "Do NOT Mess With My Mummy!" on it. He only wore it once. He only needed to wear it the once. I've known my ex since we were 11 years old - and I knew he'd get the message immediately (we prefer not to communicate face-to-face, as it upsets our son when we do).
Yes, it was passive-aggressive on my part, but it did the trick. There was no more talk of DS calling his stepmother (who is a lovely woman, by the way, who genuinely loves my son and is far better with him than my ex is) "Mummy", and no more confusion on DS' part. Which was my goal.
Although, OP, I think your future-MIL is just trying to establish a connection between your baby and your partner. The clothes are, I think, designed to be purchased by the proud/doting 'mummies' and 'daddies' to express their own "he is my hero!", "she is my princess!" opinions/thoughts/belief systems. I know a lot of grandmothers do buy them, though, because they're (a) excited, (b) proud, (c) trying to establish a connection - in their own heads, or in their extended families heads, or even for social reasons generally - between father and baby. There is no doubt that you are Mum, as far as your future-MIL is concerned... and she doesn't want anyone to doubt that your partner is the baby's Dad, so, this is what she does. Tacky as it is. And a little passive-aggressive. But if she thinks, for whatever reason, that you'll leave her son and deny him/her access to your baby...? Even though she's a lovely woman, you say, this may be her subconciously saying: "this baby belongs, partially, to my son and is my beloved grandchild... look, his babygro/tee-shirt states this fact!".