You're confusing "party loyalty standards" with identifying any would be terrorists. Neo nazis got e.g. purged from the German special forces last year.
These things are not unheard of in the US army either. VOA reported in 2019
The arrest of a U.S. soldier with far-right sympathies who is suspected of plotting an attack on American soil to spark “chaos” has highlighted a challenge for the Pentagon: purging its ranks of extremists.
Earlier this year, a U.S. Coast Guard officer who espoused white supremacist views, Christopher Paul Hasson, was arrested on firearms and drug charges outside Washington.
Hasson, an avowed admirer of Norwegian right-wing extremist Anders Breivik, whose attacks in 2011 left 77 people dead, allegedly had drafted a hit list of Democratic politicians and prominent media figures.
Prosecutors have said Hasson identified himself as a “White Nationalist for over 30 years and advocated for ‘focused violence’ in order to establish a white homeland.”
And in May, the U.S. Army said it was investigating a 22-year-old soldier for suspected ties to neo-Nazi group Atomwaffen Division.
“Our standards are clear; participation in extremist activities has never been tolerated” and is a punishable offense, Pentagon spokeswoman Jessica Maxwell told AFP. [...] “While we can’t guarantee that every person who enters the service will be free from holding extremist thoughts, various screening tools provide us the best opportunity to identify those who do not share our values,” she said.
Someone who swore to abide by the constitution but is plotting to do something contrary to that probably doesn't belong in the US army (or NG etc.)
Anti-extremism measures have been common, at least on paper, in the US army for at least 25 years; I found a report from 1996 which involved some personnel surveys etc., all triggered apparently just by the bad news of some (apparently) racially motivated murders committee by army personnel (off duty, I think). The legal basis for such anti-extremism measures, at least then, was given as
In discussing extremist activity and organizations we used the definition found
in Amy Regulation 600-20, Command Policy, paragraph 4-12, "Extremist Organizations," that:
Military personnel, duty bound to uphold the Constitution, must reject
participation in organizations which --
- Espouse supremacist causes,
- Attempt to create illegal discrimination based on race, creed, color,
gender, religion, or national origin, or
- Advocate the use of force or violence, or otherwise engage in efforts
to deprive individuals of their civil rights.
The report also discussed some proposed changes to the regulations... The 2014 iteration thereof is a lot more detailed in this regard:
a. Participation. Military personnel must reject participation in extremist organizations and activities. Extremist organizations and activities are ones that advocate—
(1) Racial, gender, or ethnic hatred or intolerance.
(2) Creating or engaging in illegal discrimination based on race, color, gender, religion, or national origin.
(3) The use of force or violence or unlawful means to deprive individuals of their rights under the United States
Constitution or the laws of the United States, or any State.
(4) Support for terrorist organizations or objectives.
(5) The use of unlawful violence or force to achieve goals that are political, religious, or ideological in nature.
(6) Expressing a duty to engage in violence against DOD or the United States in support of a terrorist or extremist
(7) Support for persons or organizations that promote or threaten the unlawful use of force or violence.
(8) Encouraging military or civilian personnel to violate laws or disobey lawful orders or regulations for the purpose
of disrupting military activities (subversion).
(9) Participating in activities advocating or teaching the overthrow of the U.S. Government by force or violence, or
seeking to alter the form of government by unconstitutional means (sedition).
b. Prohibitions. Soldiers are prohibited from the following actions in support of extremist organizations or activities.
Penalties for violations of these prohibitions include the full range of statutory and regulatory sanctions, both criminal
(UCMJ), and administrative.
(1) Participating in public demonstrations or rallies.
(2) Attending a meeting or activity with the knowledge that the meeting or activity involves an extremist cause
when on duty, when in uniform, when in a foreign country (whether on or off duty or in or out of uniform), when it
constitutes a breach of law and order, or when it is likely to result in violence or when in violation of off limits
sanctions or commander’s order.
(3) Fund raising activities.
(4) Recruiting or training members (including encouraging other Soldiers to join).
(5) Creating, organizing, or taking a visible leadership role in such an organization or activity.
(6) Distributing literature on or off a military installation, the primary purpose and content of which concerns
advocacy or support of extremist causes, organizations, or activities; and it appears that the literature presents a clear
danger to the loyalty, discipline, or morale of military personnel, or the distribution would materially interfere with the
accomplishment of a military mission.
(7) Receiving financial assistance from a person or organization who advocates terrorism, the unlawful use of force
or violence to undermine or disrupt U.S. military operations, subversion, or sedition.
(8) Browsing or visiting internet Web sites when on duty, without official sanction, that promote or advocate
violence directed against the U.S. or DOD, or that promote international terrorism or terrorist themes.