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I'm new to US politics and the Judicial Branch in the US.
First to clarify:
I know that members of the supreme court get chosen by the president and therefore often share the same political views. I'm also aware of the fact that no person can be completly objective and politically neutral.
But:
Aren't clear opinions on certain topics (e.g. abortion) hurting actual justice to be enforced? In my understanding it is the job of the Supreme Court to judge on certain cases on the base of the US constitution. But if some radical person gets chosen to join the Supreme Court, couldn't this person vote based on their personal beliefs instead of the US constitution?

Those on the Supreme Court are appointed with the "advice and consent" of the Senate, as specified in the US Constitution. In practice, this means that the President nominates a person and they go to one or more Senate hearings to be examined by the members of the Senate. Exactly what number of votes are needed to gain the consent of the Senate is up to the Senate, but currently it's a simple majority.

Once a person has been appointed to the Supreme Court, they are there for a life term. This was a provision meant to de-politicize the Supreme Court, hoping that without the threat of losing their nomination, justices would be able to rule with regard only for the law and without regard for politics. However, like all appointed officials, Supreme Court justices can be impeached, and in fact the only impeachment of a Supreme Court justice in history was on accusation of political bias in their lower court rulings (Samuel Chase). This is not something that was considered often in the past, since the court simply was not as likely to rule on political lines - most Supreme Court decisions are not decided by one vote, but there is a perception that more cases are being split 5-4 along political lines. However, even if Congress was inclined to impeach justices, I think impeaching Supreme Court members for alleged political bias in rulings would be another "nuclear option," in that whatever party does it first will be the recipient of it when the other party regains power, and you never know exactly what the future holds and whether or not one party will have enough of a majority in both houses to impeach and convict without having to cross party lines. It's also difficult to pursue, since it requires 2/3 of Senators to vote for in favor of conviction to be successful.

One more thing, in response to "Aren't clear opinions on certain topics (e.g. abortion) hurting actual justice to be enforced?" If you watch a Supreme Court hearing on a person nominated to the Supreme Court, the Senate does tend to grill them on their opinions on certain political issues. Usually, the nominee will say something to the effect of "I won't rule on a hypothetical case." This may sound like dodging the question (and is that too), but it's a good response for a judge - they do not rule based on their opinion of a topic, but based on the actual facts of the case in front of them. Even if a Supreme Court judge has a strong conviction about a political issue, a good judge does not allow their personal bias to affect their rulings.

SCOTUS famously works very well together and there are several enforced rules and traditions that get this going. But first, statistically, the 5-4 decisions are actually very rare, with the combined 5-4 and 5-3 decisions making 14% of the case decisions, compared to the 57% of cases that resulted in a 9-0 decision in the 2016-2017 session. Of the remaining cases a more stable majority is often more normal than the narrow majority (combined 29% of cases are 7-2 or 8-1). However, the reason this doesn't seem the case is that the cases that are 5-4 decisions are by their nature, very divisive topics in the United States and thus tend to get talked about more than the more boring and more firmly decided cases (Though this isn't always the case... the infamous Gay Wedding Cake case was expected to be a 5-4 decision but the court decided in a 7-2 decision.).

Now, behind the scenes, the Supreme Court get along famously and the Justices tend to be very familial with each other. Among the traditions is that they share a dinner before the State of the Union together (RBG famously attributed the wine to the reason she dozed off during an Obama speech) and will always eat lunch together when in session. This also has an added benefit to demonstrate how they form these strong bonds: The newest justice on the bench is in charge of the lunch menu and what the cafeteria makes on any given day. This actually forces the friendships, as, in order to do a successful job, the new Justice must meet with the other 8 members of the court, discuss a highly opinion driven topic (but not a very politically driven topic), and come to an agreeable solution that can satisfy all 9 justices. RBG (Ruth Bader Ginsburg) might love her some Meat Lover's deep dish pizza, but Thompson cannot stand pizza. What's poor Brett (at time of writing) to do?

RBG, who is famously one of the most liberal SCOTUS justices on the Bench was noted for her friendship with Justice Antonin Scalia, one of the most Conservative members on the bench. Their opinions rarely agreed with each other. But they were the closest friends in real life, and were frequently seen going to the Opera together as they both enjoyed the medium. She reportedly took his death very hard. The Supreme Court has a lot of internal behind the scenes tricks to impose a feeling that we can disagree, but we still get along well with each other.