Democrat and Republican are labels given without definition. You can call yourself a Republican but be pro-choice, anti-gun, and tax-and-spend. Political parties are fluid based on which politician participates at any given moment. Actual beliefs are too nuanced to be boiled down to "liberal/conservative" or "democrat/republican". Even trying to do so is making a mockery of democracy, to paraphrase George Washington. A big issue with politics is people pay more attention to the definition-less label and less attention to what the politician actually stands for (if anything).
As a non-politician with no connection to politics other than as a voter, I have consistently encountered material differences in my rights and standard of living depending on which party was in power.
Your "politicians are all the same" meme might be popular with people who are too lazy to learn about the world, but it rings hollow to anyone not living in willful ignorance.
I'm not saying politicians are all the same. I'm saying politicians are not Democrat or Republican. There is no "democrat", there is no "republican", there is a matrix of beliefs combined with a scale of how deeply held those beliefs are. You cannot say "life is better when a Democrat is in charge" because there is no definition of a Democrat. They run the spectrum, like all other politicians.
This is like saying you prefer presidents with brown hair. There are good people with brown hair, and there are bad people with brown hair.
I have Asperger's Syndrome. This rests on something hazily known as the autism spectrum. It sits alongside other disorders such as Autism and Rett syndrome. There are millions of people with such disorders. Although we all have what you might describe as "autistic characteristics", our actual problems are different, and fall into various categories that have been established to aid understanding, coping, and treatment.
Your argument that there are no Democrats or Republicans amounts to an argument that there is no Asperger's syndrome, or Rett syndrome, it's all just Autism. Anyone actually on this spectrum, or that spends even the slightest bit of time studying it, would tell you you're either ignorant or insane.
Electromagnetic energy is also on a spectrum. In some places we call it "visible light". In some places it's infrared, ultraviolet, radio, or microwave. Are they all energy? Yes, but that's irrelevant.
Democrat, Republican, Libertarian, Green, they are all a grouping of policies and beliefs that are assigned labels. There is no more "no democrat" or "no republican" than there is "no visible light".
Yet you still get "democrats" who lower taxes, start wars, and restrict liberty. Yet you still get "republicans" who raise taxes, increase the size of government, and create social programs. If you have blue visible light and mix it with red visible light, is it still called "red" or "blue"? Or is there a different name for it? Because it sure as hell isn't still blue.
If you mix a little red in with a little blue, you start shifting it out of "blue", but it's not abruptly "not blue".
No significant political party or other large group in history has ever demanded perfect adherence by all members to all aspects of platform or ideology, that doesn't mean the groups didn't exist.
I'm also not sure where you get the idea that lowering taxes is not a Democratic thing, or creating social programs is not a Republican thing. It sounds like you're getting your ideas of what the parties stand for solely from the loud-mouthed extremists.
The world is nuanced, that doesn't mean identifiable groups do not exist.
One where the majority of people refuse to see politicians as politicians. There is no Democrat vs Republican.