No. Or at least, not in the U.S. Or at least, not if you don’t play historical editor and pretend that people were wrong about what they called themselves. (Which is almost built into your definition, but since your definition may well have the same person be considered a liberal or a conservative for believing the same thing in the space of 20 years, I think I’ll stick with the standard left/right distinction.)
For example, it was our good old Democrat party that resisted the civil rights movement the most. So our liberals were wrong about
Now that liberal Democrat party has realized that that was stupid, but they didn’t learn why - they’ve decided that if anyone ever mentions the word “equality,” they must be right. And so now they don’t realize that gay marriage and abortion aren’t equality issues at all, but rather (resp) trying to create a separate thing that doesn’t and can’t exist and murdering children.
In all ages there will be things that need to change and things that don’t. Claiming that conservatism only tries to maintain the status quo is simply wrong - it’s more complicated than that. If you use that definition, the words become pretty useless. Left and right leaning seems to be relatively fixed, regardless of which one wants to change the way things are.
In fact, in the U.S. at least, I’d tend to say that it’s almost always the other way around: it’s the right leaning people that tend to want to help the poor without unjustly taking from others against their will and who want to make sure that the help is in fact help and not enabling. It is the right side that wants to make sure there is no discrimination based on being of a minority race, but doesn’t want to change this into discrimination against those of the majority race. It is the right side that doesn’t want want the government to force people into religious practices, but doesn’t want to try to shut religion out of the public square entirely. It is the right side that realizes that “gay marriage” is not the same as real marriage and that we shouldn’t pretend that it is, and it is only the right side that realizes that it’s a bad thing to kill children.
Of course, our right side isn’t perfect. But it’s certainly not the opposite.