When it stops asking questions, making hypotheses, and pointing out the existing evidence, and starts telling you what you should do and believe based on the evidence. Regardless of what's healthy for you, or what works for you, or what kind of person you are.
It's not offensive to not worship a deity, and to self-identify as an atheist ("without-gods-ist"). Choosing to worship or not worship is a personal choice.
It's extremely offensive to tell someone how they should make that personal choice, and to insist that only you have the right answers to theological questions like "what is god?" and "how should I relate to her?"
Whether your answers to those questions come from a religious or atheistic background, simply having different answers to questions of pure theology is not in and of itself offensive. For instance,
It's not offensive to look at the available evidence, both in neurology and in people's self-reported experiences of divinity, and conclude that gods are probably names people give to feelings and experiences they have and concepts that they revere. But,
It's extremely offensive to tell me that, because this is what you've decided my deity is, you don't believe she exists. Because for me and many others, she does.
My relationship with Inari Okami is one of the most important ones in my life. She literally saved my life at one point, just by talking to me and being there when I needed her. She may not be that important to most of the people in the world, who barely acknowledge the kami of foxes and rice (even if they like both of those things). But to me, she is in some ways closer than family, and has been in my life longer than any of my partners or adopted family members.
I have chosen to be agnostic with regards to the question of how Inari exists. Because whatever the "true" answer to that question is -- assuming there is one -- it doesn't affect my relationship with her.
This isn't a case of "blinding myself to the evidence." I am fascinated by the evidence, and the neuroscience behind theological experiences. I regularly discuss the divine on a purely material level, and even have at least one materialist explanation for how and why I am otherkin.
It's simply a case where the theory doesn't affect the practice, sort of like how the mechanics of why I'm transgender don't affect the fact that I need to transition. For whatever reason, praying to Inari works for me. Focusing on her presence and listening for her (spiritual) voice is an effective meditation, which helps calm me and clear my thoughts of distractions. I am often reminded of things I needed to do, or helped to realize a new way of seeing something, while praying to her. The fact that I subjectively experience this as Inari telling me these things doesn't change that, and if anything means that my current approach to prayer works.
Conflating my experiences with those of movie and TV show characters who "hear voices in their heads," or implying that I am in any way dangerous because I both pray and listen for answers to prayer, is blindingly ignorant and offensive. It negates my personal experiences, replacing them with a Hollywood stereotype that bears no resemblance to my life. And it causes me material harm by diminishing my credibility, my ability to say what I go through and have others believe me, which I already have problems with on account of being female, trans*, and disabled (not to mention a plural system and otherkin).
Atheists know better than most what it's like to be seen as a scary and dangerous person, just because of what goes on in their heads. They don't need to make the world worse for other people who are marginalized because of religion.