The majority of tinctures are made with alcohol. The alcohol in tinctures is crucial for extracting the active ingredients of a herb or homeopathic remedy, as well as stabilizing and preserving them. Alcohol acts as a carrier substance conveying active ingredients within the body.
The amount you physically give is minute so unless you're dealing with an animal who has organ damage or alcohol sensitivities it's generally very safe. If you have concerns, you may want to look into herbal products, not tinctures, as you won't really find many good quality tinctures without alcohol as the base.
Here is a blurb from Canine Herbalist, Rita Hogan, that she wrote in regards to another query about alcohol-based tinctures…
"I've been a dog herbalist for almost 20 years now (just so you know I'm not just saying this randomly) and I can assure you that the amount of alcohol used as a preservative is safe for your dog when used as recommended.
There are approx. 1200 drops in, for example, the Jump For JOYnts bottle. The alcohol percentage per drop is minuscule making the serving less than 0.5% alcohol. I would recommend avoiding for dogs with seizures that are sensitive to alcohol as a trigger which I've come across in my practice."
Also, because it's homeopathic, Julie Anne Lee DCH RCSHom, founder and formulator for Adored Beast, recommends you can dilute it with water…
"Historical standards of practice to deliver homeopathic remedies have always been in an alcohol base. If you’re concerned - use the required amount of pumps into a half glass of water, stir with a spoon, and use 1 teaspoon right away, and it will be equally as effective. How can that possibly be? The reason it’s in an alcohol base is to preserve the efficacy of the remedy, when it’s delivered right away (after being mixed with water) it’s equally as effective."