Probably not.  As a matter of federal tax law, charities and social welfare organizations are not prohibited from purchasing alcohol for their events and activities.  I mention social welfare organizations because many volunteer fire departments are tax-exempt as social welfare organizations under section 501(c)(4) of the Tax Code.  (The IRS has ruled that contributions made to (c)(4) departments for public purposes are also tax deductible, even though gifts to (c)(4)s are generally not deductible.)

Conceivably, one could argue that providing alcohol on a regular basis to your members could result in their private benefit or private inurement, but it doesn’t sound as though you would be providing enough to the entire group that it would be considered private benefit or inurement that would jeopardize your exempt status. 

According to a report for the National Fire Protection Association released last year, there were an estimated 1,080,800 firefighters in the U.S. in 2019, with 722,800 of them (67%) being volunteers and protecting about 70% of the population.  The nation is currently losing volunteer firefighters at a significant rate and responses to emergency calls are being delayed all over the country.  One of the attractions of belonging to a volunteer fire department is the social connection with others in the community.  I would argue that there is a public interest in promoting that cohesion.  If a little beer is helpful in promoting that camaraderie and keeping volunteer firefighters involved, it is far less costly than having to replace the volunteers with paid members.

You obviously have to be careful that your members are not impaired when responding to a call, both for their safety and that of the public.  You may not be able, under state law, to provide alcohol to under-age members.  Although not likely, you might live in a “dry” county where you can’t buy the alcohol, but that shouldn’t prevent you from getting it elsewhere and drinking it locally.  Handled judiciously, I am not aware of any law that would be violated merely by paying for beer and alcohol.