It is cultural, but not written SOP, in my airline for the PM to read out wind components from the FMC - when relevant, or when requested by the PF.
Same here. I think you’d be foolish not to take them into consideration.
Would I initiate a go-around based solely on FMS data? Yes, especially on a tighter/contaminated runway. A GA is generally a non-jeopardy manoeuvre - the same can’t be said of ending up on the stopway or grass, or setting the brakes alight.
I threw an approach away at 50’ in the Caribbean some time ago as it just didn’t seem right with a “calm” wind reported. FDR later showed 23kts tail!