There is no contradiction. There are two ideal cases, neither of which shows up in real households, although tendencies in both directions do show up at times.
Household loads are almost never linear resistors. Their impedance varies, both with line voltage and with other factors.
Although most load impedances vary, only a few vary in such a way so as to draw something approaching constant power.
There are sources of information for each individual kind of load you might encounter in a house - all separately, of course - if you need that level of detail.
Heating elements, including incandescent lights, increase in resistance as the voltage increases, but not enough to make them constant-current. They just don't appear to follow Ohm's law because their resistance changes with current.
Most small-scale electronics approximate constant-current loads, but the actual power consumed is trivial.
Larger items with switching power supplies (computers, game systems, TVs, monitors, video gear, etc.) may approximate constant-power operation over as much as a 90-250v input range.
Most of the current drawn by many electronic devices is delivered to their load or wasted as heat in the attempt, and it varies widely for reasons other than line voltage. A rock band in the basement with ugly-but-efficient digital equipment can draw kilowatts on program peaks, dropping to dozens of watts during silence. A microwave oven on half-power just turns full power on and off every few seconds.
Electric motors, though, do often draw more current as their voltage is decreased. Not perfectly consuming constant power, but trending in that direction. It doesn't often affect households, but construction workers using long extension cords are familiar with the effect, where the voltage decrease comes from line losses.
Typical household loads are often dominated by a few large electric heaters that turn on and off at random, so to speak. When they're all off, the remaining load can be quite different, and very small. If the result of a 5% increase in line voltage is that twenty kilowatts of electric heat in the floors get warm enough to all turn off at once, the current will certainly go down, but it's not exactly Ohm's law.
The rare situations where a large load may increase current with decreased voltage include an electric car charger pushing a constant charging current into a large battery, a server farm (racks containing dozens of constant-power computers), or a busy wood shop with a large number of big electric motors running at once.