@Barry2021,
One word --- "petty". This is all stupid petty stuff that you should overlook. Yes, you are set in your ways and so is she.
I agree with you if this bothers you to speak with her about it. Do just like you did, please tell me if you open something or use something of mine. I know that does not bother you but it does bother me so please just let me know.
That's it. That is all you should have to do.
But on the flip side I am with your wife on this - if I had something that I used predominately and say my husband has another brand he prefers - if I found my new bottle/container open - I would assume it was my husband that opened it. It is a logical assumption; then later I would verify with him or he with me if unsure. It should not be this huge issue.
And if it bothers you that much, put it somewhere she typically would not have as easy access. That way if she runs out - she won't have anything and will quickly learn she needs to replace her stuff before it runs out.
As others said - it is surprising you are married to each other.