This is about a 2-year-old child. His parents scream and shout at each other frequently - like thrice a week. How will this affect the toddler?
I'm going to assume that these aren't domestic abuse but loud disagreements of a more or less civil nature. Witnessing domestic abuse is bad for kids and well studied.
Toddlers will model their caregivers. If their people shout at each other it should be expected that the kid will try it too, and since that is generally not tolerated in kids they may get frustrated.
Fighting often takes a lot of attention, and toddlers generally really like attention. If the toddler is able to identify a trigger in a caregiver they may exploit it to receive extra attention.
Toddlers like their people. When their people don't seem to like each other they can become confused about who their people are. This can mean they try to take sides, and if they do it may be hard to get them comfortable with the other person again.
Conflict resolution is also something learnable by modeling. If the conflicts are not a problem in themselves or causing problems for the kid, it may be a way to teach de-escalation and any appropriate rituals of reconciliation.
Young kids are really trying to become copies of their people; if this is behavior you don't want them to have stop it.
Speaking from experience, it does nothing productive for the child. Doesn't matter if they're 2, younger or older.
Being in an environment where shouting is a regular occurrence can lead to a number of different possible developmental issues which can be reversed in time and with maturity but not having it happen in the first place is obviously the most desired outcome.
Children shouldn't be taught by example that shouting is a productive way to do anything other than getting urgent information out when absolutely required i.e in an emergency or if it's just so loud around you can't hear each other.
You don't agree with someone? Reasoned debate and keep it friendly as you can, it's not a conflict it's a discussion- shouting isn't going to fix anything. Raising your voice escalates, it rarely de-escalates- with few exceptions.
Seeing your parents argue or shout is also scary as a small child- if it happens so often you get desensitized to it that's even worse. It can be an ongoing thing that they'll be terrified of what's going on- as your parents are meant to be a stable, solid foundation- seeing them in conflict like that is daunting. It raises uncertainties that are uncomfortable and hard for a child to process and this comes down to the most important thing of all:
Norms. No child, ever, should be subjected to believing that the "norm" is for their parents to be in conflict. They'll take this model and apply it to their own life if they can't realise that it isn't correct. Sometimes this can occur subconsciously and be passed on unintentionally, but this shouldn't happen full stop.
If parents disagree, well fine this happens- nothing wrong with that. However it's how they deal with that disagreement and process it- talking like adults, reasoning it over, debate and discussion- not shouting, will resolve issues. I can only hope that things are being resolved and this isn't the same thing over and over, as a demonstration that talking things over resolves issues rather than a recurring shouting match just goes to prove that shouting fixes nothing, whoever shouts the longest or loudest wins- or that this is normal.
None of this is good.
I think it does harm because the child does not feel safe. A child that is insecure can have delays and emotional problems, but that is usually only in extremes. A friend has court awarded custody of her granddaughter because her daughter and her grand's father were in an abusive relationship and the child suffers separation anxiety and other problems.
On edit: That was a verbally abusive relationship. It was extreme, though.
@not store bought dirt -- got it right. We model how to act and problem-solve for our children. We lead by example. If people are constantly not working out their differences and fighting, that is what they are teaching.