In this part of the world, around the rim of the mediterranean, olive oils is very definitely used to dress a salad. This is not usually done by emulsifying everything in a shaker though. Generally, the salad is seasoned with salt and pepper, then drizzled generously with olive oil and a little lemon juice or good wine/balsamic vinegar. This allows the flavour of the oil to stand, and it is nicely complemented by the other secondary flavours.
Olive oil is also used to complement the flavour of fish, baked in foil in the oven after being brushed with olive oil and seasonings. This imparts a special aroma and flavour to the fish.
The best, and simplest in my opinion, is when for supper or breakfast we just slice some vegetables (cucumbers, tomatoes, peppers, carrots) and drizzle them with olive oil, to be eaten as part of the meal.
It's certainly safe. Butter, Oil, whatever, it's more about taste than anything else. Some people even push lard and butter as the "safe" options, because they require less processing than oil, and much less than margarine.
One thing which you should be aware of in regards to butter vs oil: butter has a significant amount of water in it, so you shouldn't substitute 1-to-1, or you will have a stronger flavour (and more fat) than perhaps you want.
If you're accustomed to salted butter, adding some salt will help ease the transition. If the flavour of olive oil is off-putting, there are plenty of more neutral flavoured oils that have a similar fat composition, or you can simply avoid extra virgin olive oil*.
*extra virgin olive oil in the U.S is largely a scam. In most of the world (countries that adhere to the IOC standard) this signifies "First Cold Press" olive oil. In the US it signifies "lamp grade olive oil with green food coloring". There are no restrictions on the use of terms like "extra virgin" in the US, so you can't guarantee that's what you're really getting just because it's on the label.
Best Answer
Don't make any emulsion sauces with olive oil. The high speed of dispersion, especially with an electric blender, creates unpleasant bitter compounds in the oil. But frequently, even the speed of a hand whisk is high enough to ruin the taste. Either that, or you are too slow to create the emulsion at all.
You can form yolk-fat-emulsion sauces with practically any fat, and olive oil is an unfortunate exception with its taste change. Just choose another fat compatible with your diet. From a purist's point of view, they won't be a Bearnaise, the French sauces are very tightly classified. You will also get an obvious difference in taste (only butter tastes like butter), and, if you are using a liquid oil, a slight difference in handling - you can let a liquid-oil-emulsion cool down, while a butter or lard based sauce will harden into an unpleasant grainy mass.
If your base food is very plain/bland tasting, you can play with subtle oil tastes to create an interesting effect where the main "seasoning" is the oil in the sauce.