My wife is highly arachnophobic, so my group has had to handle this in the past.
Our system is pretty simple. Rather than replacing the creatures, we use a set of code words: spiders are now sheep. Everyone, including my wife, knows what the words really mean. But because we keep them consistent among themselves, it offers each player a choice: mentally edit the spiders into place, or accept that despite appearances, these are not ordinary "sheep". The death-sheep from Hell are dangerous beings to run away from really fast, and so while my wife's experience may be slightly sillier to visualize, the difference is only slight.
- spider ->→ sheep
- web ->→ wool (you can even speak of spinning both of these)
- entangling in a web ->→ knitting a sweater
The "sheep" have a nasty, venomous bite, and unlike ordinary sheep they could lay eggs from which lambs hatch. We keep these details, because, yet again, these are not ordinary sheep (and even in the real world sheep bites can be pretty nasty, even though there is no venom).
In practice, this seems to work well. The fact that the words are slightly ridiculous if taken at face-value makes it easier for the players to mentally edit the spiders they really are back into place, should they choose. But the fact that the words are somewhat consistent with one another makes it easier for players to leave the death-sheep in place, if they want: there is still some sense of verisimilitude.
On the other hand, it may not work well for everybody. I can't speak for all arachnophobes. Some may not be willing or able to accept the sheep at face value when they know what the words mean. Still, I suggest giving it a try: since it doesn't involve changing any mechanics, it's probably the simplest thing you could do, if it works for your players. If it doesn't work, there are plenty of other answers here to try, but this one probably involves the least amount of work if it actually works.
