I'm currently taking minocycline for my skin. Is it bad if I drink alcohol while taking this medicine?

Not a good idea. Minocycline may interfere with alcohol. It is a good idea to limit your alcohol intake for the period of time that you are on minocycline. Check with your prescribing physician to confirm what they recommend and what to look for when alcohol and minocycline are combined.
Yes. Are we talking one can of beer on the weekends watching football, or drinking a six pack or more a day? Alcohol can affect the metabolism of many drugs, and is not good for acne to begin with. Minocycline has some potential effects on the liver, as does alcohol. Talk to your doctor. Small amounts of alcohol (one or two drinks no more than one or two times a week prob ok, more is not).
No/Yes. There is no significant interaction of ethanol with minocycline. However, one should drink in moderation with only one to two ounces of liquor per day or equivalent. Your skin wold most likely do better off any ethanol. I woluld recommend you abstain and see the results.