In brief, you are correct [if I am interpreting the question correctly], but other factors mean that your neighbor should probably get the blue canopy.

While neither color will "attract" heat from the sun, the white canopy should be cooler. The color of an object/material is determined by the wavelengths of light which are not absorbed (i.e., those that are reflected or transmitted). Eyes can only detect the light which is there, and absorbed light is no longer "traveling around" to reach the sight receptors. White light, sunlight being one example, comprises light with wavelengths in the visible spectrum in approximately equal fractions. Any object (such as the tent canopy) which reflects all of those wavelengths appear white. In contrast, an object which reflects only some of those wavelengths will have a different color which depends on the wavelengths reflected. The blue color of the second canopy means that the visible light in the "blue" portion of the spectrum is reflected; the light of other wavelengths is absorbed. Absorbing this light transfers energy to the fabric of the canopy, raising the temperature. [Aside - color does not affect absorption of infrared light, commonly thought of as heat. Any heating due to light in that regime will be approximately the same between the two canopies and can be omitted from consideration here.]

However, this does not mean that your neighbor should get the white canopy. Although the temperature of the canopy (meaning the material of the tent) will likely be higher for the blue than for the white, the same may not be true of the people underneath it. The white canopy will absorb less light, meaning also that it will emit less heat, than the blue canopy. (Note that this is because the blue canopy is warmer, not due to a relation between color [visible light] and thermal emissivity [infrared light]: white and blue canopies of the same temperature would emit nearly the same amount of thermal energy.) A person very close to the canopy would feel warmer with the blue canopy than with the white one. However, while the white canopy absorbs less light, one consequence is that it transmits more light than the blue canopy (see links above). The transmitted light will then reach and be absorbed by the people and furniture underneath the canopy, heating them directly. In other words, the blue canopy will block more of the sun's light (be darker or "shadier") than the white canopy.

The temperature under the canopy ultimately depends on the combination of the heating due to emission from the canopy material and that from the transmitted light. If the tent is open such that a breeze can get through, then the air warmed by the hotter blue canopy will not reach the occupants. This is essentially the same as the principle which keeps Bedouins cool despite their wearing black clothing. In this case, the blue canopy, which blocks more of the transmitted light, will likely give a cooler tent despite the tent fabric itself being warmer. Given that many people use electronic devices outside, your neighbor might also consider that readability of screens will be better with the lower transmitted light of the blue canopy. In addition, darker colors may offer better protection from UV light.

White will reflect more light than blue, but white will also emit less light than blue. Overall, I'd say that white is probably better, but it's probably going to depend in part on how reflective the two tents are in the infrared and ultraviolet, too, so I'm not sure what the best answer is.

Yup - white reflects heat. Darker colors absorb heat. I 'like' the experience, barefoot in a hot outdoor parking lot, when the white lines are cooler than the black parking spaces.

On the other hand, there is this question: "Why do Bedouins wear black robes in hot deserts?" here

So maybe your neighbors can purchase which ever color they prefer, because "The additional heat absorbed by the black robe was lost before it reached the skin."

That is correct! The color that appears on an object is the color that object is reflecting. Green grass, for example, reflects green light. However, it also means that the object is absorbing every other color. So green grass is absorbing red, blue, yellow, and every other color that it isn’t. Color in this case is a form of light, and light is a form of energy, and energy produces heat. So you can imagine the more colors absorbed by the object, the hotter the object gets. Pure black and white are interesting, however. Black absorbs all color wavelengths and white absorbs none.

Now let’s look at your specific question. A blue canopy is going to reflect blue light, but absorb red, green, yellow, orange, purple, and every other wavelength of color. White however is special, because it reflects every wavelength of light and absorbs none. This means that white will reflect the most light and is the best option for keeping the deck cool!

You are correct. Colors of things are based on the wavelength of light it reflects. The different wavelengths of visible light combine into white light. So, a white object reflects all wavelengths of visible light, while a blue object will only reflect the blue wavelength of light, and absorb radiation from all the other wavelengths.