Rolling out at 300ft in a jet is dodgy; ironic, isn't it that on a gin-clear day the stabilised approach criteria is 500ft, when the weather is cr@p, it's only 300ft? BTW, 3.5° is 4 whites on the PAPI. "Go Around!"
Well, I still have to be stabilized in 500 feet (on speed, engines spooled, configured, checklist completed on correct lateral and vertical path). Only thing that is allowed to be an open "item" until 300 feet is wings level. Ironic? Yes I agree. Dodgy, no. But extra vigilance is definitely required.
PAPI indication alone is not a reason for go around. Especially 4 whites, which would steadily correct toward 2 white. As long as sink rate doesn't exceed 1000 fpm and aim point stays fixed on the windscreen (PAPI to be disregard below 200 feet anyway according to my OM-A, following the other active thread about it for another official reference).
At a certain airport we fly to, where we often fly visuals, the PAPI is so weak, that during daytime you won't see it until the last 500 feet. And if you follow it, it will take you in too high, so my assumption is that it is additionally calibrated wrong. I usually brief that I will fly 2.5 to 3 deg degs visual path, as recommended by Boeing, and to disregard the PAPI when it becomes visible. It often shows 4 reds, and I don't go around for that either.
So I think it is a matter to be conscious about such indications and plan and brief for them in advance. If it would be a surprise, and cause for wonder, why I see 4 white or red, for sure I will go around too.