The treasure companion has stone as -30 OB and -30 strength (so a significantly increased chance of breakage).
RMU doesn't list stone, but for the weaker metals it lists (gold, silver, copper), the penalty is reduced for blunt weapons. E.g. gold is -30 but -20 for blunt, silver -20 but -10 for blunt. So if -30 seems excessive, it might be -30 for axes but -20 for blunt weapons like maces.
Actually, if you look at Table 2-49: Other Materials in the beta Treasure Law, you will see that flint weapons are -15 and obsidian weapons are -10 where these substitute where metal would be used normally (-15 when substituting for metal, but +5 for obsidian partly offsets). However, in the given setting, I would advise setting flint to the +0 base for convenience and treating all metal weapons as bonus items.
It is, of course, up to the GM to determine what weapons can reasonably be given stone equivalents (rapier, I think not).
RMU gives +5 for obsidian but no bonus to its durability (and I think a strength penalty would not be inappropriate). Obsidian can have extremely sharp edges, but they may not last. Flint is +0.
Okay, you saw the table, so I don't know why you'd say RMU doesn't list stone. It doesn't list it under metals, because it isn't metal. Flint has been so widely used on Earth, there wasn't much cause to detail inferior stone, given RM is usually Iron Age+.
Very early spears and arrows were wood with fire-hardened tips. Maybe -30? The best pre-metal tips are flint or obsidian, tied on probably with sinew.
I can't find any numbers for bone. Your -20 does not seem unreasonable.
Organic materials are going to vary a fair amount. A bone club might well be better than a wooden club. It depends on the bone and the wood. In the given setting, I'd probably adjust the modifiers for AT as well. A bone arrowhead will penetrate human flesh pretty well, but armoring hides or even heavy furs should protect better than against a hard metal edge, so I'd use a minor penalty, if any, again AT-1 and make it less useful against more armored targets. There are also other organic materials that can and have been made into parts of weapons. This starts to get into the kind of details that you need to work out in specific settings. I don't think I'd allow bone edges larger than a dagger or handaxe at all, unless you got hold a special materials. It's not much of a cutting or even hacking material, best for puncturing weapons.
Bonuses for wood are listed in Treasure Law. I set ash as the default (+0). Substituting wood for metal tacks on an extra -20, so carving a head on an ash club to create an ash mace gives a -20 mace. If recalibrating to a flint standard, I'd reduce that to -10. There isn't enough basis for trying to make a general distinction between wood and bone, so a standard of -20 for bone seems good (though with more restrictions on how it may be used... wood is more easily shaped to a given purpose).
Guidelines in the Alchemy Companion have bone as -20, wood as -30, and stone as -50. That GM's should merely use this as a guide to set their own modifiers for specific materials is stated in the table itself, and I think that the ordering itself is suspect. Bone and wood are common materials, but did not generally replace stone. Rather, the opposite. Fire-hardened wood points gave way to flint spearheads, then to better flint spearheads, then eventually metal.
Considerations of realism aside, what does the game benefit from? Well, making it harder to kill anything by putting a blanket penalty across common weapons seems like a bad idea, which is why I'd reset to a "flint standard" and let basic stone weapons be your +0 base. You need to decide which weapons will even be available. Short bows would be very likely, long bows less so. Composite bows are pretty advanced and unlikely. Crossbows are out. I would probably split modifiers for materials in a (largely) pre-metal setting to allow different modifiers for puncture, crush, and cutting weapons. When so many weapons will be made of "non-standard" materials, the differences become more important. I would also, as mentioned above, look at varying modifiers against different armors (metal armors may not be a consideration, but some animals have formidable natural armor). As characters are more likely to be making, rather than purchasing, weapons in a primitive setting, adding more complexity (more flavor and more opportunities to work out ways to take advantage of the system) makes sense. You could use obtaining suitable material for some project a driver for an adventure. Somebody wants a shark-tooth-edge sword? Time for a trip to the coast! Or to obtain the rare feathers to trade for the shark teeth, depending on how the GM and players choose to go about things.
TL;DR - Make it as complex as you and the players will have fun with, don't get too hung up on making it "realistic", and try to turn the need for materials into plot hooks.