If we are talking about stainless steel machining, I do not think that chromium oxides formed by passivation on the surface of stainless or acid-resistant steel are a significant cause of tool dullness during machining. This is an extremely thin layer, especially in the first moments.
According to available information, the most important reasons for difficulties during machining of alloy chromium steels include:
1. The cause is chromium itself, its high content in this steel - theoretically minimum of 11%, and most often above 13% (popular stainless steels) or even 18% (acid-resistant steels, e.g. 304, 1H18N9, which is what I use most often). Chromium is a very hard metal, sources says that hardness ranges from 40HRC to even 68HRC (hard chrome plating).
2. Poor thermal conductivity of stainless/acid-resistant steel - it can be even several times worse than ordinary carbon steel. This in turn causes rapid overheating of the cutting edges with insufficient cooling/lubrication - a fact that is especially common in amateur machining. This property of this steel is also "unpleasant" when welding 304/316 type steel - it causes large deformations of welded details.
3. These steels relatively easily form build-up on the cutting edges, which creates difficulties in cutting and dulls (by overheating) the tools.
4. Additionally, in acid-resistant austenitic steels (with low carbon content, i.e. non-hardening 304, 316, etc.) small amounts of chromium carbides can form (precipitate) in the cutting area - and we all know what the hardness of carbides is.
To simplify as much as possible
: from my experience - the most important thing when machining stainless/acid-resistant steel is
low cutting speed and CONTINUOUS cooling/
lubrication: i.e. pour the coolant, pour it and pour it again
Then even ordinary HSS steel tools (and even more so HSS Co) will work for in stainless steel a long time.