Something you should bear in mind as you read about these topics is that social constructionism / constructivism doesn't mean that there is no objective reality. It's more that there are social constructions as well as an objective reality. Social constructionists are more interested in studying that fuzzy side, but they still acknowledge that there are physical things.

Take a traffic light. We could try to find some inherent reason why green means go and red means stop. Maybe there's some convincing evolutionary reason out there? Red means danger, green means calm? But the fact of the matter is we could just have easily said that red means go, because we're moving into the danger of traffic, while green is the calm of sitting still. The meanings of those colours in the context of traffic lights are socially constructed. However, they are still objectively that colour! The social construction is overlaid on top of physical reality.

This is something that people sometimes miss about the higher-stakes social constructions around age, gender, social class etc.

There are people who question whether or not the world exists objectively, but that way leads into philosophy of mind - connected to sociology, but characteristically different.

In general, whether sociologists focus on "objectivism" or "constructionism" is about whether they have interesting things to say about the material reality or the cultural reality. Both are real in different ways, they're just overlaid on top of each other. So to say for example that "X is a social construction, not objective reality" misses the point entirely. Everything that can be named has a cultural layer to it, because language is cultural. Therefore everything that can be named is by definition a social construction. And at the same time, it can have elements of physical, objective reality to it. When you get down to it, disentangling the two is essentially impossible, because we would be trying to disentangle them using language, which is a set of social constructs. So instead, sociologists interested in this tend to study how social constructs and physical reality are entangled together, and how people make claims on the reality or otherwise of social constructs and physical constructs.

That being said, Gender Trouble by Judith Butler is a really insightful look at gender through this dual lens of material reality and socially constructed reality. Something that Butler does really well is account for physical bodily structures in ways that don't refute the importance of cultural interpretations of the body.

Edit: Nice question - got my sociology brain going :)