It is not inherently rude to decline an offered drink, whatever the reason, although it is entirely possible to decline a drink in a rude way. However, that does not mean that the person offering the drink will not take offense to their offer being turned down. Someone offering you a drink believes they are doing something good for you and may take offense at having their good graces turned down, regardless of the reason. But the denial of their expectations does not make it rude. It is more rude for someone to continually offer you drinks after you have declined than it is to decline a drink, as many women can likely attest.