If you are replacing strings with the same gauge. You probably will not need to reintonate.
If you have found that over time your intonation has been going further and further out you might need to tweak the truss rod.

Seancasler is right.

I've been playing quality electric and acoustic instruments since the late 80s, and have been doing all my set ups, etc... on my own.
Too much of a major ordeal is made out of tuning and intonation, and one thing where I feel the M.Megatar people got it right on was with their Buzz Felten tuning, where things are not as they appear to be from a strobe tuner standpoint - but yet work perfectly with the ears.

It's all good !!
Cheers.............

Seancasler is right on the compromise and imperfection, however ... i think it is a mistake to use the 'perfection is impossible' fact to justify giving up on using a good method to intonate, which is what i am explaining. I am assuming that a player wants reasonable intonation across all the played pitches. I only give the very best advice because i assume someone wants to intonate well.

I have studied Just Intonation in depth, it is not relevant in this context because the intent is to get as close to 12 Tone Equal Temperament as possible (in all this i am assuming that is the target, because it usually is).

2 frets an octave apart is unnecessary, better to use the lowest and highest played frets if you must only check 2 pitches, but 3 or more is better.

In fact, not enough of an ordeal is made of intonation, because (being a guitar technician and a qualified physicist who has studied the science of music, Just Intonation, historical tuning systems) i have discovered that most of the common intonation advice for guitars is a little sloppy and is based on misunderstandings.

One common problem people have in setting their intonation on tapping instruments is bad technique. If you pull the string away from its axis the resulting note will be sharp when you tap (or pluck) it.

Make sure you are tapping along the string axis (use hand motion).

Also, with low-tension strings, it's always best to check the instrument in playing position rather than laying it down, unless you have a bench setup that provides support under the middle and ends of the instrument. Any pushing (or pulling) on the ends of the instrument from underneath, even just from gravity, will give you different results.

Make sure your truss is adjusted properly, because higher action means stretching strings, which will also affect your intonation.

Tappy New Year!

IX and Greg.

All good and valid points.

My point is really to just to try to simplify and demystify this as much as possible.

Intonation is and should be a basic skill that everybody should feel comfortable doing themselves. Unfortunately, it seems like too many people are intimidated to the point of being unwilling to give it a shot.