I actually already gave a few examples of this: the UK Conservatives invoke the "good-old-days" all the time.
I don't quite grasp why the responsibility rests on me to prove the Republicans don't represent founding principles, when you were first claiming that they did, and you haven't bothered to provide any actual similarities or points of continuation. But I'll have a quick look:
* Sidney Powell attempted, late last year, to have entire states' Electoral College votes discounted, conflicting egregiously with the founding principle of democratic elections;
* The last Republican President held numerous private financial interests, and enriched himself from his office in various ways, in contravention of the spirit of the emoluments clause;
* The Republicans' longstanding efforts to restrict immigration would seem at odds with the founding intention for the US to act as a welcoming nation of immigrants fleeing tyranny overseas;
* The Constitution clearly intended all budgetary decision-making to come from Congress, yet the last Republican administration aimed to fund the border wall by... diverting the security budget?
* The Constitution envisages the Judiciary as a distinct branch of government, outside political influence of the others; yet both parties have transformed the Supreme Court into a political tug-o'-war;
* The right to free protest is, of course, a founding principle. Yet Republicans have long supported extensive crackdowns on protests, and the last Republican President famously had peaceful protesters cleared with tear-gas so he could set up a photo op.
* The separation of Church and State is a founding principle, yet we have numerous instances of the Republicans pushing that back.
* The US was founded explicitly on the Rule of Law, but law-breaking has been common, from Nixon to the breaking of international law through arms sales and indiscriminate bombings.
Finally, I very much doubt the Founding Fathers envisaged the US as a global swat-team, toppling democratically-elected leaders in Latin American countries, installing puppet regimes, or launching invasions to bring about regime change.
You know my stance on Trump, so I'm going to bypass the Trump-dependent claims here. It doesn't do us much good for me to say "I don't think Trump is representative of the Republican Party" a bunch of times.
The other points:
* Republicans have a century+ of trying to manage immigration. That is not always to limit it, it's only limit in the sense that at certain times, the flow of immigration to the US has been beyond management. But other times, managing immigration involves things like a path to citizens for undocumented immigrants, which Bush wanted to do, and Reagan actually did, and hell Trump would have gotten DACA into actual legislation if they let him have a wall. I don't think the Republican Party is anti-immigrant.
* Democrats made the Supreme Court into a political tug-of-war. Prior to the Roberts Court was the Rehnquist Court, which had as many as 8/9 Republican appointees on it, and yet remained politically independent. The Court declared school prayer unconstitutional, upheld affirmative action, and struck down state laws banning late-term abortion, and it was 7-8 Republican appointees deep. But it maintained political independence because Bush, Reagan, and Nixon appointed good, impartial justices (excepting Clarence Thomas, but I'm not gonna complain about that). Republicans started fighting to get judicial appointments when Democrats made clear that their appointees were not going to be impartial, although that fight was mostly held on the lower courts.
*The right to peaceful protest is in the Bill of Rights, yes. Congress shall make no law abridging the right of the people peaceably to assemble, or to petition the Government for a redress of grievances. They did not write peaceably by accident, so I have no doubt at all that the people who wrote that would have no protest against laws against violent assembly. Yes, including property damage.
*The separation of church and state exists in the founding principles for the protection of the church from the state. It's there to ensure people's free exercise of their religious beliefs. Republicans hammer on about protecting people's religious freedom constantly. That's basically a 1-to-1 transplant, and I do not see the distinction.
*Law breaking is common, I will concede that. But everyone falls short of their ideals. I will not argue the Republican Party is successful and enacting, or even personally practicing, the Republican image of government. But in the end we are all sinners, nobody is the ideal version of themselves, so I would never say that the ideal doesn't exist because it isn't reached.
And finally, the US as a global swat-team is mostly a Democratic thing, that outside of Bush seems misplaced to aim at Republicans, especially now when the push to get out of foreign military entanglements is strong on the right.