Baby grabbing stuff

😱👏🏽😱👏🏽😱

My almost 5 month old has developed an interest and ability to grab things. She also expresses curiosity and excitement about objects (and our cat and dog). My husband has been letting the baby touch the cat (he helps her pet) and has also been taking her around the house letting her grab/touch household objects like a hanging lamp, my clothing hanging on a rack, my jewelry stand, etc. I get that he’s just keeping her occupied but I worry that by letting her touch things that I dont want her touching when she’s no longer in arms (and thus under our control) we are setting a bad precedent. I would rather her be introduced to her stuff, like toys, or books, or cups.

My fear is that as a SAHM I will be dealing with a bigger baby who is frustrated by limits I set around what she can play with/touch. But I understand that babies her age might be too young to form habits? So maybe it doesn’t matter if she’s being carried around the house to grab everything that strikes her as interesting right now because she’ll have no memory later. Anyway, I was hoping someone might give me perspective on this before I go asking my husband to do something different and risk offending him or being controlling/micromanaging.