If we removed all environmental protections around the world, what would be the most important species to go completely extinct?

Bees. And then finally stupid humans

Homo Sapians

Plankton

Primary producers (photo-synthesizers and chemo synthesizers). All other life gets energy from them.

Edited in response to OP's edit.

Algae. It makes more than half of our breathable oxygen, some studies say up to 70ish%.

The most important single species? I don't think there is one. Pretty much any one species disappearing would have its niche filled by another. There are a number of fragile ecosystems where that wouldn't happen and there would be a local collapse, but those would not have large-scale impacts.

If all environmental protections were removed, we'd see broad destruction of the environment across many species. Think broad deforestation, mining, waterway contamination, air pollution. It wouldn't be species, it'd be whole ecosystems killed.

Most important to humans?

Humans.

Really if all protections were removed, the soil, water, and air would be so badly polluted with heavy metals, radiation, etc., from large corporations dumping that we wouldn't have the ability to grow enough food, probably within a generation or so. Long before climate change dealt its deadly blow. And the wealthy who survive that won't have enough servants to keep them alive for too long.

Most important to the Earth?

That would be more interesting and it would be really difficult to pick just one. Probably something like Prochlorococcus which is one of a few ocean plankton that produce the most oxygen on Earth. That will die off much sooner than Humans from climate change as the ocean temperatures and acidity are rising more quickly than the air.

As a side note, one thing I think a lot of people miss from the movie Soylent Green,...

::: spoiler spoilers in here ... but was always the more interesting thing than the, "Soylent Green is people!", for me, was the research that Sol was doing and why he ended up ending his life. The oceans were effectively dead. Not much can recover after that, at least not quickly enough for humans to survive without some massive efforts which would be unlikely as we'd first resort to wars that would devastate our ability to do so.

:::

Realistically : bees and other polinetor

We don't know enough, the whole biology on earth doesn't know enough to say for sure:

"We could definitely do without this species, or that"

Mosquitos.

Implicit in your question is the assumption that environmental protections are effective, or that they’re even based on any objective importance criteria, apart from say economic importance.