Because it ended before finger-snap. From IGN

"It seems like our finale ended pre-snap," star Clark Gregg told IGN when we caught up with the man behind Coulson earlier this week.

Avoiding Thanos' snap altogether was probably the smartest play for Agents of SHIELD, especially considering that, according to Gregg, "We never know at the end of the season if we’ll do another one, and we didn’t know this time, and this was very much written as a conclusion and it felt that way." Ending with half of our heroes disintegrating certainly would've been a bummer if the show had been canceled - it was upsetting enough in Infinity War, even knowing that we have Avengers 4 on the horizon to hopefully fix Thanos' mess. But you can't help but feel like it was a little bit of a cop-out after Graviton namedropped Thanos several times in episode 20.

But season 6 has got green-light so it can get answer in that if Avengers: Infinity War effected them or not and in which way.

Even the showrunner were not sure if they are getting new season and not and they said this:

With official confirmation still awaited, Agents Of S.H.I.E.L.D.'s showrunner team of Jed Whedon, Jeffrey Bell and Maurissa Tancharoen have claimed that "The End" would work as a satisfying conclusion to the show as a whole if another season wasn't green-lit. Speaking with Digital Spy, Tancharoen states:

"We approach the end of every season the same way, which is... we never really know if we're going to get another one until we're towards the end of our shooting anyway, so our goal is to be able to satisfy either way."

So ending it with Thanos's finger snap will look like a bad idea if they don't get next season.

As mentioned by V2Blast in comments, EW have interview of the makers and it seems date rescheduling was responsible too:

ENTERTAINMENT WEEKLY: You guys had been hinting at possibly incorporating the Infinity War ending. Why didn’t we see that in the finale?

JED WHEDON: There’s some of that we can’t answer.

JEFF BELL: Part of what happened was, they changed the release date.

WHEDON: Yeah.

BELL: And we move at a different schedule than they do and so suddenly everything was a week earlier, and so we had to make some adjustments and that’s how we end up with our story.

WHEDON: Right. And the other thing is that there’s certain story points that are so — there would really be no way for us to address it and keep our show intact. Given that there’s another movie coming out, and there’s gonna be constant repercussions of their universe, so what we felt was that the safe play for our story, and for the integrity of our universe, was to operate outside of it.

BELL: To acknowledge it was happening, but that we had our own problems and we’re dealing with that.

WHEDON: Right, and also the timeline is a little bit fudged in that we assume that the last couple of episodes of our show take place during Infinity War. We’re running in a lot of real-time at the end of the season.

MAURISSA TANCHAROEN: The last four [episodes] all in real-time.

** WHEDON:** Yeah, so we sort of thought of it as these events are still ongoing as our season ends.

What would that mean if the show is renewed? Is the team somehow magically exempt from Thanos’ snap?

WHEDON: Yeah, well what we like is painting ourselves into a corner, so that the problem we face is not that our show went off the air, it’s that it’s back on the air. “Oh no, now what?” Yeah, so we’ll have to figure out how that plays, and it’ll depend on what the season looks like and our air dates and all that. So, yeah, that’s a bridge we’ll have to cross.

BELL: We call it a classy problem.

So we just have to wait for next season to see if Thanos's finger snap had any impact or not.

To answer your question on the timeline of the Aos finale... the episodes 19-22 were considered to be occurring in a span of a day or two based on this interview with the showrunners...

BELL | There are a couple things at play. They changed the film’s release date [to a week earlier]. And if you really look at the movie, an alien ship shows up in New York, and they show up in Wakanda, so in terms of the world’s perception, it’d be very easy to be elsewhere and to not be fully overwhelmed with what’s happening. Now the very end of the movie is a different story, and there’s a world where our [season] has ended before that happens.

WHEDON | We think of our last few episodes taking place during the film…. [Episodes] 19 through 22 are pretty much one day. Also, one of the things that we tried to do was even if we’re just hinting at a crossover, our concept was to create motivation for our villain, for our antagonist — using the events of Infinity War and using the larger MCU battle to sort of inform [Talbot’s] motivation to become what he’s becoming. That was our main tie-in, trying to drive our own antagonist. We felt like that was a good way to deal with it, but keep the things in our world in our story.

Besides season 6 was not on the horizon until the last moment and so season 5 finale was shot as a series finale and the "snappening" might have undercut the moment and would have been an unresolved cliffhanger if AoS was cancelled...

The current episodes were before the finger snap took place. Perhaps more time had passed between the battle in Wakanda and the finger snap that we are led to believe. Also, not everyone disappeared at the same time. Not sure how that works, but perhaps the finger snap just hadn't "caught up" with the characters in Agents of Shield. As with all of the future marvel movies coming out, we'll have to see how the characters are affected post-snap in season 6.

According to the show's creators, Season 6 deliberately ignores the events of the Snap and its aftermath. It takes place one year after Season 5, which should put it after the Snap, but no references are made to the event.

This article provides a multitude of reasons for this, courtesy of Marvel TV head Jeph Loeb and showrunner Jed Whedon:

• They didn't know how to depict a post-Snap Earth, as it hadn't been seen in the MCU at the time they were filming, and they didn't want to contradict Endgame by accident (which means, yes, they're not contradicting it deliberately. Go figure)
• They didn't want the show to get bogged down in depicting what the world looked like post-Snap (or indeed, post-Endgame), and wanted to focus on storytelling instead
• They didn't want to tie the show into Endgame in case the network changed its air date and they ended up spoiling parts of the film before it had been released

The article also provides a possible justification for how the Snap might never have happened in the Agents of SHIELD continuity:

...the fifth season catapulted the show some 90 years into the future, then sent them back to the present in an effort to alter the course of history. So it’s possible the timeline changed into one that wasn’t among the 14 million possible futures that Dr. Strange saw.

In other words, it's possible (though not confirmed) that Agents of SHIELD now takes place in an alternate continuity where the Snap never happened.