In a comparative manner of speaking, when we look back at the expedition team in Prometheus, they removed their helmets as soon as they found the air to be breathable, without explicitly screening for pathogens.
Ford: Jesus. The sunlight is heating the water. Check out the humidity.
Charlie: Yeah, look at the CO2 levels. Outside it's completely toxic, and in here there's nothing. It's breathable.
Elizabeth: What are you doing? Charlie don't be an idiot.
Charlie: Hey don't be a skeptic. Right, there's something generating an atmosphere. David?
David: Dr. Holloway is correct.
Ford: Cleaner than Earth actually.
Charlie: They were terraforming here.
Elizabeth: Please don't do...
Charlie: I'm not wearing this thing anymore.
If this is how experts act like in the new Alien universe, a civilian team is naturally less prudent with safety.
However, Ford (the medic) did use the phrase "cleaner than Earth", and Charlie did check his instruments before removing his helmet. So giving them the benefit of doubt, we may assume their instruments screen for toxins and pathogens automatically, in addition to atmospheric composition.
Fast-forward to Alien: Covenant.
Soon after they arrived at the planet:
Ricks: Tox level within tolerances.
Right after they have landed:
Mother: Confirming atmospheric composition. Oxygen 19.5%. Nitrogen 79.4%. Barometric pressure 15.4 Psi.
And... they opened the door.
That's pretty much it.
But in "Prologue: Last Supper" when the crew was toasting before cryo, Daniels mentioned that Covenant was the first ever large-scale colonization mission to come this far into our galaxy. This implied that there were likely to be smaller scale colonization missions previously, since a moment earlier Rosenthal said:
I heard about these crazy bugs just outside this colonial post. Apparently they look like cockroaches the size of a giant poodle.
So humanity have encountered alien life before. Thus it is safe to assume that they are aware of alien pathogens and there are protocols in place to deal with alien lifeforms. For instance, there is a Med Bay in the Lander and there are quarantine protocols to handle such infections... after they've been exposed, instead of prevention. After all, chances that alien pathogens being compatible with human physiology, are slim.
Aside from in-universe explanations, removing helmets is an often-used artistic license just like doctors not wearing masks in films, to let the audience better see the face of the characters. Alien: Covenant is a survival horror movie, a science fiction, but not science documentary. Try not to pay too much attention to these things and enjoy the movie!