No true scotsman fallacies are not even needed, Hitler was not a socialist
Hitler was a Socialist - in particular he was a National Socialist, which, he stated, was
based in Marxism, though with an added racial component, and which was one of many branches of general left-wing thought that sprang up in the latter 19th and early 20th Centuries.
So-named in contrast to
International Socialists (such as Bolsheviks) who argued that the distinctions that truly mattered were class-based and that therefore the global proletariat was a single interest group,
National Socialists imported Living State theory (which held that Nations were like biological organisms) and argued that National Identity was a major distinction that mattered, and that therefore their brand of Socialism would be pursued within each nation, rather than attempting in a COMINTERN like manner to create some kind of International Joining of Hands. An International Socialist slogan was that The Proletariat Had No Fatherland. National Socialists rejected that formulation.
As stated above, the Nazi Party (which is one party, but only one party, within the much broader National Socialist Movement)
Platform included some pretty obvious call-outs to their intellectual home on the left, notably:
...7. We demand that the State shall above all undertake to ensure that every citizen shall have the possibility of living decently and earning a livelihood....
...9. All citizens must possess equal rights and duties.
10. The first duty of every citizen must be to work mentally or physically. No individual shall do any work that offends against the interest of the community to the benefit of all.
Therefore we demand:
11. That all unearned income, and all income that does not arise from work, be abolished.
12. Since every war imposes on the people fearful sacrifices in blood and treasure, all personal profit arising from the war must be regarded as treason to the people. We therefore demand the total confiscation of all war profits.
13. We demand the nationalization of all trusts.
14. We demand profit-sharing in large industries.
15. We demand a generous increase in old-age pensions.
16. We demand the creation and maintenance of a sound middle-class, the immediate communalization of large stores which will be rented cheaply to small tradespeople, and the strongest consideration must be given to ensure that small traders shall deliver the supplies needed by the State, the provinces and municipalities.
17. We demand an agrarian reform in accordance with our national requirements, and the enactment of a law to expropriate the owners without compensation of any land needed for the common purpose. The abolition of ground rents, and the prohibition of all speculation in land.
18. We demand that ruthless war be waged against those who work to the injury of the common welfare. Traitors, usurers, profiteers, etc., are to be punished with death, regardless of creed or race.
None of which are exactly what you call the Classic Liberalism that Conservatism "conserves" today, nor anything you'd call an example of "capitalism".
Nazis and Hitler especially are habitual liars and will happily lie about their positions to gain power. Their modern counterparts frequently pretend to care about free speech, they hide their positions to soften them, and talk about adopting leftist rhetoric to pull people in.
I'm not aware of National Socialists ever being in favor of Free Speech as an individual and inalienable right. Quite the opposite, in fact:
23. We demand that there be a legal campaign against those who propagate deliberate political lies and disseminate them through the press. In order to make possible the creation of a German press, we demand:
(a) All editors and their assistants on newspapers published in the German language shall be German citizens.
(b) Non-German newspapers shall only be published with the express permission of the State. They must not be published in the German language.
(c) All financial interests in or in any way affecting German newspapers shall be forbidden to non-Germans by law, and we demand that the punishment for transgressing this law be the immediate suppression of the newspaper and the expulsion of the non-Germans from the Reich.
Newspapers transgressing against the common welfare shall be suppressed. We demand legal action against those tendencies in art and literature that have a disruptive influence upon the life of our folk, and that any organizations that offend against the foregoing demands shall be dissolved.