Beard oil is generally composed of a blend of carrier oils and natural essential oils, and are used on the beard and the skin underneath it. So it is generally safe to use, and there are no bad effects that come with it. But this is not always the case. Some people can have an allergic reaction, where the skin is irritated due to the potent composition of the essential oils. This is rare though. But it still happens.
So the best way to determine if your skin is happy with the beard oil is to simply apply a small amount on your arm. Don’t use it on your face directly if you feel like you can have a reaction to it. So just leave it on your arm for a while and if nothing happens, then you can use it on your beard. But again, this is very rare. So generally you have nothing to worry about.
For people who have reactions to beard oil, simply use a type that has a small amount of essential oil, or an unscented version. This would be the best way to go, since there would be a small amount of essential oil in the unscented beard oil. The bottom line is that the oil is usually natural and organic, so it is considered safe for the most part. Even in the rare case where you get a skin reaction, this is usually temporary and goes away on its own. I have a lot of bearded friends, and I have never witnessed any of them who had an issue with using beard oil. But just in case, it is always better to stay safe and check for skin irritation by testing a small amount on your arm first. Then you would be good to go!