with his tactical brilliance

Forgive me for going a bit off-topic here, but I would strongly disagree with this claim. Washington lost most of the battles and campaigns he fought, and the highest praise he was given at the time was that he "retreated in a European fashion" after being defeated. Washington's strength lay in being able to hold together a poorly trained and poorly equipped army in very difficult circumstances, not in actual tactical or strategic skill.

By contemporary or modern standards, where on the spectrums of politi al ideology did/does/would he stand?

His first term (1789 - 1793) saw relatively minimal party (or "faction" as they called it then) fragmentation and conflict, mostly due to both the fear and uncertainty held by American politicians over whether their new republic would last, and also out of reverence for Washington; they all respected him so much they didn't want to disrupt or weaken his presidency by devolving into petty party politics. That said, there were certainly different views on how the government and country should progress, and by the end of Washington's first term and into the second these different views would begin to solidify into distinct factions - it would be inaccurate to call them parties, since at this point there was still no official party system in the US, just loose associations of like-minded politicians, roughly comparable to the populares and optimates in the Roman Republic.

The Federalists were led by Alexander Hamilton, who was Washington's Secretary of the Treasury. He was strongly in favour of centralising power within the executive branch (i.e. the presidency) and thus minimising the role of both the legislature and also the individual states. He believed that if the states had too much autonomy it would inevitably lead to disunity and weakness, which would in turn leave the country vulnerable to either internal fragmentation or foreign invasion. He started his Federalist agenda by having the federal government assume the debts of all the states incurred during the war (arguably the issue that first started the Federalist vs. Anti-Federalist split). He continued to institute further centralising policies such as establishing a national bank and raising tariffs for imported goods. The Federalists were also marked by a general preference for friendly relations with Great Britain rather than with France. Hamilton elaborated on this and said that the stronger trade potential and political stability of Britain would be in the US's interests rather than the chaos of the French Revolution, its political instability and the constant warring. This preference for Britain was shared also by John Adams, another prominent Federalist leader (and also the ambassador to Britain at one point). The Federalists drew much of their support from banks and big businesses, and saw the future US prosperity and strength as deriving from international trade and modern financing methods.

The Anti-Federalists, as one might imagine, took the opposite views to the Federalists on many issues. They were led by James Madison and Thomas Jefferson (although the latter was the less public figure, and more behind-the-scenes). As the two leading Virginian politicians, they were strongly in favour of greater state autonomy and power (understandable considering Virginia was the largest and most influential state). They were horrified at what they saw as the encroachment of the federal government on traditional states' rights, especially on the issues of debt, finance and trade. They generally saw the Union as a confederation of states rather than a single unified nation. They were also generally opposed to any overtures to Great Britain, and saw them as their traditional enemy. They favoured closer relations with the French because of their historic friendship (this would only change when Napoleon rose to power and overthrew the republican government). The Anti-Federalists drew much of their support from the 'planters' (i.e. men that owned large estates with slaves), as the South was less urbanised and economically sophisticated than the North. These planters were basically their own social rank, roughly equivalent to the lower aristocracy in the Old World, and held considerable influence in both state and federal politics. The Anti-Federalists saw the future US prosperity and strength as deriving from maintaining and expanding the wealth and influence of the planters.

As to which of these factions Washington belonged to, or sympathised with, he himself never openly declared for one or the other, wishing ardently to maintain the visage of neutrality and non-partisanship, but both privately and through his policies he was a Federalist. He allowed Hamilton to have an enormous influence on him and his government's policies, to the point where some historians have even gone so far as to say Hamilton was the "prime minister" of the US and the real driving force behind much of Washington's agenda. In almost every instance of a Federalist vs. Anti-Federalist issue, Washington ended up coming down on the Federalist side, while attempting, sometimes futilely, to assure the Anti-Federalists he was unbiased. Washington said in private correspondence that he agreed with Hamilton and the Federalists that the federal government and the executive branch must be strong and powerful, perhaps influenced by his military background. Arguably Washington's greatest achievement was his adamant refusal to become involved in European affairs during the French Revolutionary Wars, despite the increasingly insistent rhetoric by prominent Anti-Federalists such as Jefferson (the ambassador to France). This pleased the Federalists, as well as Washington's willingness to establish friendly relations with the British. In Washington's second term it became increasingly apparent where his true political allegiance lay, and Anti-Federalists felt confident enough to publicly criticise him about his Federalist agenda, something nobody would have dared to do during his first presidency. But the hero aura of his wartime leadership had faded, and the nitty gritty political maneuvering had become a bigger issue. Washington and Hamilton weeded out the Anti-Federalists from Washington's cabinet until eventually by the end Jefferson was the only one left, and after many failed attempts to turn Washington to a less Federalist stance, he saw the writing on the wall and resigned, bitterly saying that Washington was basically Hamilton's puppet at this point (he was somewhat right).

Issues that define left-wing and right-wing parties in the US in the modern day such as immigration and social welfare practically didn't exist in the late 18th century, so it's impossible to draw comparisons there. The issues that divided the factions/parties were almost purely political and economic, not social.

Feel free to go off topic, I never learned of the Washington of the Revolutionary War in school so my knowledge of Washington is independent and trivial.

Thank you so much for your long and in depth response.

His impartiality and being able to hold differently idealed people together is impressive.