If you think about it, Time, it's feasible that MIL probably didn't see a banana as 'food', more as a snack or even treat. It was possibly the most healthful, baby-friendly consumable that she had. MIL possibly forgot herself in that the baby had been fed and that he wasn't eating solids yet. The fact that she gave a whole banana made me think of it as something for 'teething/gumming', something safe to put in his mouth.
Should MIL have done this? Possibly not, particularly as OP said that she had instructed no solids. MIL possibly thought of banana 'mush' as not a solid, but a semi-solid and therefore ok.
The fact that OP posts as if MIL takes no notice of her, did this behind her back, doesn't trust MIL with 'her' baby anymore... well it speaks volumes to me. There is another post on the board where an OP perceived that MIL had given children alcohol - not so - OP checked and all is well. This is different, very different and it's not like Tango's situation either - that was terrible.
OP is not the sole 'owner' of the baby; her husband also has a say. To ask him to take his mother to task and put her straight isn't an adult thing to do. I know of many mothers who seem to behave as if their views trump their partners' views when it comes to child-rearing. They don't - although they partially get their wish when it comes to custody and the child(ren) is in their care for part of the week.
Children never do understand the minutiae behind a parent's decision to limit or thwart contact with family members... they just know that they don't have a relationship and they'd probably like one. I was such a child as were my brothers. My mother's argument with my grandmother's sister (not sure what relationship that is?) soured a whole branch of the family tree. My mother laments that we are a small family. Not worth it as far as I'm concerned.
I really do feel strongly about these MIL-fixing threads and I never think the whole picture is as is portrayed, merely that it's 'my way or the highway' in many cases and that is never reasonable.