should the chain be uniformly tight on a fixie?
A little bit of variation is normal, yes. If the chain is so loose at the loose point that the chain falls off I'd call that a manufacturing or assembly defect and take the bike back to where you bought it and get them to fix it.

In more detail the issue is exactly centering the chainring on the bottom bracket/crank, where normally the chainring is not perfectly round or perfectly centred. You can often tweak this a little by slightly loosening the chainring bolts and using the tiny amount of play between the chainring and spider to get a slightly better fit. Loosen the bolts, rotate the crank to the tightest point, pull on the chain to shift the chainring, repeat. You'll almost certainly not be able to entirely fix the problem, but you will probably be able to reduce it.