This is a common question from new and experienced floaters alike. We've heard both sides argued, with decent arguments on both sides. Even with all of the opinions out there, we stand behind the fact that you should always shower before a float.
One of the main reasons you should shower before entering the tank is that it's common courtesy to be as clean as possible before entering a public tank. But if you're at a commercial float center, do you really want to enter a tank where the stranger before you left their deodorant, hair gel, lotions, and sweat in the water?
Commercial float centers utilize large filtration systems and water treatments that will aide in maintaining cleanliness, but let's not make that process any more difficult than it needs to be. A quick shower before floating is an easy and reliable method of keeping things clean. The shampoos and body washes at float centers do not contain any lotions or oils, so they're perfect to rinse off beforehand.
There is one more scenario, however. A personally owned, personally maintained, home float tank is another story all together. Go ahead and do whatever you're most comfortable with.