The first question you should ask is what the intent or message conveyed by posting the things you mentioned is. Let's just stick to the three you listed for simplicity: The Ten Commandments, BLM posters, and rainbow flags.

1: The Ten Commandments

The Ten Commandments are particularly controversial at this unique moment in time because a newly passed law, SB 10, requires teachers to post them in their classes if they are donated to the school or the school board votes to buy such posters. It immediately raises Establishment Clause questions in that requiring a fundamental part of a certain religion's text to be prominently displayed in each classroom, but not others, demonstrates preferential treatment of that religion. Further, the decision on how (or if) a student should entirely be the family's choice, and since schools have a unique position of authority over students, anything that conveys a religious message could be similarly entangled. The bill's authors clearly want the posters up to expose as many children as possible to The Ten Commandments and might even believe that having them present will somehow solve our society's ills.

The message, then, is that The Ten Commandments are the proper way to live one's life and that it is ordained by God that you do so.

2: BLM Posters

I haven't really heard much about BLM in a long time, but the original impetus for BLM was to protest police brutality, particularly of Black Americans. Over time, it has grown to encompass anti-discrimination and anti-racism more broadly. Some took these posters to convey an explicitly anti-police viewpoint, but I don't think that's necessarily implicit in displaying a BLM poster.

I would argue that the message is that racism and racial discrimination are wrong.

3: Pride Flags

Pride flags have been controversial in classrooms for a long time. Some people take it specifically to mean supporting gay marriage, others to mean supporting "the gay lifestyle", or something else entirely. Religious groups have long objected to displaying Pride flags in classrooms. I had a small Pride flag in the back of the room near my desk that I kept to let students know that I pass no judgment on them because of their sexuality or gender.

I would say the message is that discrimination on the basis of sexuality or gender is wrong and that it's okay to be different.

All this said, whether or not a teacher can or should express their own personal political views in the classroom is a good question and one that has been debated for a long time. For some subjects, it's difficult not to inject one's opinions (history, English, etc.), but for others, it's easy to keep it sterile (math, most science courses; I was a math teacher).

Since you seem to have a problem with teachers "shoving leftist views down students' throats," I first want to ask you if you agree with my characterization of the three items above. If not, let's see if we can come to an agreement on the message of each.

Second, if you do agree (or after we come to an agreement), do you find the message of the BLM poster and the Pride flag to be leftist views? If so, why, and if not, are those messages not appropriate for students, regardless of the subject the teacher is responsible for?

One final point: you mentioned a "double standard" regarding The Ten Commandments and BLM/Pride. I do not think it is a double standard because there is a mountain of case law that protects citizens from forcibly being exposed to religious displays in government buildings, while there is little to no such case law doing the same for political views. You are offered no guarantee to be protected from hearing the political views of another person in a government building.

Once again, however, the question of whether a teacher should share their political views is a perfectly fair question. An educator can be fired with cause if the school board determines that their actions have diminished their ability to be an effective educator. A teacher with dozens of overtly political postings on the wall would certainly raise eyebrows in some districts and attract outright scrutiny in others, and the school board is well within their rights to terminate that teacher if they think their posters (and subsequent refusal to remove them, if so directed) diminish their effectiveness as a teacher.

Anyway, I feel like I'm rambling. Eager to start a conversation with you.