I think one key factor is that driving is not a right, but rather regarded as a privilege. If you fail to meet the guidelines surrounding that privilege, it can be revoked.
Another consideration is that rights of others who use a public road; does someone who uses a public road while at a reduced capacity to properly operate a vehicle violate the privilege of others on the road? Does such a person infringe on another's right to life, liberty, and the pursuit of happiness? Maybe it's the rights of responsible drivers that is really being infringed upon by drunk drivers?
Ah, but what if someone is not drunk?
If I read correctly what has been posted here, the real bone of contention is over when can the police stop a citizen and assess their ability to operate a vehicle. If given probable cause, then there is no argument, or so I presume. Could we say that some of us are concerned over the idea of stopping anyone -- without cause -- to asses their condition to safely operate a vehicle on public roads? Seems so.
As someone else said, the higher courts consider it fair so long as everyone who passes a checkpoint is subject to the same scrutiny...i.e., an officer is not acting on his/her own discretion.
This is an important thing to debate -- without getting political (remaining philosophical) -- as our hobby can involve becoming impaired while consuming the fruits of our labor.
Unless we all agree to learn to brew non-alcoholic beer?
Edit: Sorry to say I am PUI..."posting under the influence"...I've been drinking Bud Light, Sweetwater IPA, and homebrewed American Brown Ale. Forgive me?