Masonite is steam-pressed wood, which means the lignin will acidify your print and degrade it in the long term. I don't know how long that takes but it's at least a couple of decades as I've seen 30-year-old prints mounted like that with no issues.
If you do some googling for wet mounting of fibre prints, there are a few people who recommend coating masonite with a thin (2x diluted) layer of PVA glue, letting that dry then slapping a dripping-wet fibre print onto the masonite. The water reactivates the PVA layer (which will wick into the FB) and the print will dry/shrink onto the board for a perfectly flat finish without needing a drymount press. I suspect it's great for exhibiting on the cheap but probably not archival. If I were going to mount a 30x40" print, that is absolutely what I would do, at least for my first try I'd also like to experiment with putting a bit of sodium bicarbonate into the PVA to help neutralise things, but I don't really have the time nor the facilities to determine whether that would make things worse.
If you're not doing drymount but want archival results, do not use contact adhesives, especially the spray ones. Quite apart from the respiratory hazard, they're very not-archival. Having said that, I use contact adhesive myself when I have a smaller print I want to put on the wall for a few years and don't really care that it will prevent the print outlasting me (50-60 more years at most). In my case, prints are either for-the-wall (exposed to house fumes and not expected to be particularly archival), or they're for-posterity, unmounted in a box and treated comparatively very well.
Edit: I suspect that a layering of masonite, cotton rag and then FB print would be archival. The lignin isn't going to make it through a buffered wood-free mount board, and the masonite (with reinforcing as suggested above) will provide rigidity. You could assemble it all with PVA, which *is* archival, especially if you get the bookbinding version with antimicrobial agents. Plants will eat your PVA otherwise.