This is exactly what frightens me about Poison/Fire. Having 7 resists and immunity to two of the most popular status effects tips this typing from "bad" to "good", in my opinion. Furthermore, it takes away the best part of doing a mono-Poison type: it gives CAP3 a way around Steel-type Pokemon. If it we give it a strong offensive Poison-type STAB, it can just abuse that and use Fire-type attacks as coverage. It doesn't seem like much of a challenge to make Poison/Fire good.
Let's take a look at the 7 resistances for Fire/Poison, because taken in isolation it's just a number and doesn't really tell us anything.
4x Grass: Celebi and Virizion commonly carry moves that threaten Fire/Poison super-effectively. It is a good answer to variants of Venusaur and most Breloom and Ferrothorn however.
4x Bug: There are only three Bug type Pokemon in OU and only two of them use Bug type attacks. However Fire/Poison is a fantastic counter to them: Scizor, Volcarona and Forretress. Bug type attacks seen on other Pokemon is almost always U-turn, make of that what you will.
2x Steel: This is more of a resistance 'on paper' because Steel type moves aren't commonly seen on most Steel types. Fire/Poison is still notable for countering or checking the vast majority of Steel types however including Mr #1 Scizor, Ferrothorn, Jirachi (most variants), Skarmory, Magnezone, Forretress and Lucario. However it must be wary of switching into Metagross while Heatran is a hard counter and commonly carries Earth Power.
2x Ice: The two Ice Pokemon in OU are Mamoswine and Cloyster, and they both threaten Fire/Poison with a super effective STAB move.
2x Fighting: Fire/Poison is not going to feel safe switching into any Fighting type that commonly carries a strong Rock move. This includes Terrakion, Conkeldurr, Mienshao, Virizion and Infernape. Terrakion is in fact a hard counter. It is a good answer to Breloom, Lucario, Toxicroak and Scrafty.
2x Poison: This is a resistance on paper because no Pokemon commonly uses Poison type moves in OU and Tentacruel is a hard counter. It will threaten Toxicroak however.
2x Fire: There are four Fire Pokemon in OU. One, Heatran, is a hard counter; Infernape threatens with Stone Edge, but Fire/Poison is a good answer to Ninetales and Volcarona.
That was a list of all the types of Pokemon that Fire/Poison 'resists' or is supposed to be good against. What we find is that it's quite a mixed bag, and Fire/Poison will not be handily switching in as often as its '7 resistances' may suggest. In fact the only type that Fire/Poison can consistently threaten is Steel and Bug.
Fire/Poison is not great defensively, it often won't be able to switch in safely to types even if it 'resists'. However it can consistently switch into Steel and Bug types, and this is where the dual typing shines. Once it has grabbed that opportunity to come in safely, its neutral coverage acts as a great deterant to help it establish its presence.
Its list of hard counters in OU reads as: Heatran, Tyranitar, Terrakion, Tentacruel, Jellicent and Gastrodon.
Of course this analysis was considering typing alone and stats or movepool will affect its performance greatly.
In summary: Fire/Poison cannot switch in safely to the vast majority of the OU metagame; it can't even switch in against most of the types that it 'resists' and it has a 4x weakness to Ground that can be taken advantage of. It can be demonstrated to be a pretty 'bad' defensive typing. However it can consistently switch in easily against Steel types and that is the only type it can feel safe to switch in against and it is reliable at it. It's 'good' offensive coverage only comes into play when it is safely switched in, which no one can deny is a good offensive typing. It also has common hard counters in OU by typing alone.
I hope someone can do an analysis like this of other typings being discussed, I'd love to see some comparisons made. I hope that's where this discussion will go, to really analyse and compare what we have on the table. Again I'd like to say in closing that I'd be happy to see a Fire, Ice or Poison type go through. Giving the right tools to a lesser used type is what draws me most to this concept.