That framing is distracting us from the authoritarian vs civil liberties issues, which is a dangerous and immediate threat to our ability to have any significant political influence of any kind.
If a conservative wants to preserve some status quo, basically all policy they use (and have available as a tool) in a permanently changing and developing world (socially, technologically) is that of restrictions, especially on civil rights, and of authoritarian mechanisms like police power. For weird reasons, conservatives never* want to preserve status quo civil rights like workers rights, freedom of information rights and similar that are anti-authoritatian.
This can change in the future, as it has before, but in 2026, even libertarians only care about personal freedom for a certain class of people.
In Spain (you can see this in the website) our traditional left and right parties are largely in favor, while the parties in both ends of the spectrum (at the lack of better term: far left and far right) seem to be largely against.
The sad thing is that it seems that the parties that are already established or likely to alternative in power are the ones that are pushing for it, and this makes it very difficult to fight against
there is more than one left wing faction in the eu - we got greens (more radical and oppose chat control), s&d (mainstream parties like german spd, mostly support), the left (hardcore socialist/communists) and renew europe (centrist liberals). none of them are completely united on this.
far right parties are also against chat control most of the time. christian parties (moderate right wing) support it for moral reasons. its really more of a establishment/alternative issue than left/right.