Alcohol is present is many products as a solvent or carrier. You can read more detail here: Fiqh of Ethanol.
Alcohol in such products will generally be halal, 1. if it’s ethanol then the below will be considered, 2. if its methanol or another form of alcohol then such products do not intoxicate thus exempt.
In summary, the ruling is based on the source of the alcohol not being from dates or grapes, else it would be impure conclusively and haram. If from another substance or synthetic, then the following four conditions need to be met:
- It is not being used to intoxicate
Alcohol is not used to intoxicate
- Not being used as intoxicants are used
Nor used to make the consumer drunk
- Not being used in an amount that intoxicates
The amount is incredibly at low levels, less than 0.1%.
- Not being used for vain purposes
The alcohol is not added for a vain purpose in such products. The alcohol in mouthwash also destroys almost all the bacteria in your mouth – both the bad and good bacteria.
The majority of such products meet this guideline.