Okay, so the question is somewhat flawed in the premise, and that makes it kind of hard to answer.

So, first of all, let me comment on this section, in which you apply modern modes of thinking onto the past:

From a cynical, hyper-pragmatic point of view, I wonder why did the British reject those proposals. [...] Or did they actually care that much about democracy? You may say they didn't want to join the Nazis because they were brutal mass killers, but it's not like the British Empire was all respect for human life and dignity, given how they killed and enslaved millions of people in their conquered lands. So what was really driving their struggle against Germany?

Apparently, your idea of cynical hyper-pragmatism is one of almost video game esque Machiavellian power politics where all that matters is the maintenance and eventual increase of your own power base. This vision will serve you well if you wanna play Sid Meier's Civilization 6, but it doesn't translate into history.

In real life, people have ideals that they aren't willing to cross. The reason why your hyper-pragmatic gut reaction might make sense is because the struggle for power is the ideal of the fascist, but your premise is flawed in so far as to assume that to further your power is a goal that is continuously active and universally beneficial. And your comment on how the British Empire didn't respect human life and dignity is by the way straight-out-of-the-book Nazi apologia. It is an argument used by authors like Schultze-Rhonhof and Mohner.

It is true that the British did horrible things in their imperial territories, but the 'democratic' zeitgeist of that time simply didn't view imperial subjects as equal to the imperial motherland's population. As such, imperial ambition or the desire to presevere as an empire does not seemlessly translate into a natural desire to adopt fascism as a political or social ideology to guide your nation's principles. A British citizen could hold both anti-fascist thought and believe in democracy, as well as opposing any sort of emancipation of His Majesty's subjects in Kenya or India. Nowadays, we view this as hypocrisy - and it is. But back then, this "doublethink", to use the Orwellian term, was perfectly valid. It wasn't mutually exclusive to be in favor of democracy and in favor of the empire.

Okay, with that out of the way, onto the question itself.

Next to the hindsight flaw, the question also contains at least partial historical inconsistencies. You say this:

He even promised to send the German army to protect the British colonies in exchange for British support in the sea against America. [...] They would've kept their Empire. [...] did they not trust Germany?

The last question obviously implying that the British didn't have a reason not to trust Germany. Well, I tried to look up when that 'promise to protect the British Empire' came about and in what context. Well, the context is the aftermath of the dissolution of Czechoslovakia and the onset of the Invasion of Poland.

At 1.30 p.m. Hitler talked to the British ambassador, Nevile Henderson, and he put on a very good act; he declared that he wanted to live on good terms with Britain, that he would personally guarantee its world empire, that Germany’s colonial demands were limited and that his offer of a general settlement would follow the solution of the Polish–German disputes, which in any case he was determined to settle. This, he emphasised, was his last offer. He overdid it a little, stretching credulity too far by confiding to Henderson that once the Polish question was out of the way he would conclude his life as an artist and not as a war-maker.

[Grenville, p. 236] (General History)

An SS guard of honour stood stiffly to attention as British Ambassador, Sir Nevile Henderson, arrived to hear the Führer extend an olive branch one final time. For an hour, the upright yet meek Henderson was subjected to one of Hitler’s monologues railing against British and Polish intrigues. How dare an Empire totalling more than forty million square kilometres try to impose its will on a nation of just 600,000 square kilometres. 'It is quite clear who it is who desires to conquer the world,' the Führer sneered. He wanted no 'bloody and incalculable war' with Britain for such a conflict 'would be bloodier than that of 1914 – 1918'. But the Polish problem had to be solved – and would be solved; there had been twenty-one incidents on the Polish-German frontier overnight. Such an intolerable situation could not persist, for he was, Hitler told the ambassador, 'a man of great decisions'. He was willing to negotiate, but his patience was running out. This was his final offer. It was an offer, Nevile Henderson suggested to London, worth considering.

[Hargreaves, p. 95] (Military History)

For what Hitler had to say was quite preposterous. He “accepted” the British Empire, he told the ambassador, and was ready “to pledge himself personally to its continued existence and to commit the power of the German Reich for this.

He desired [Hitler explained] to make a move toward England which should be as decisive as the move towards Russia ... The Fuehrer is ready to conclude agreements with England which would not only guarantee the existence of the British Empire in all circumstances so far as Germany is concerned, but would also if necessary assure the British Empire of German assistance regardless of where such assistance should be necessary.

He would also be ready, he added, "to accept a reasonable limitation of armaments" and to regard the Reich’s western frontiers as final.

[Shirer, p. 548] (General History, Diplomatic Focus)

Henderson handed Hitler a translation of the British reply to his 'offer' of 25 August at 10.30p.m. that evening, the 28th. Ribbentrop and Schmidt were there. Hitler and Henderson spoke for over an hour. For once, Hitler neither interrupted, nor harangued Henderson. He was, according to the British Ambassador, polite, reasonable, and not angered by what he read. The 'friendly atmosphere' noted by Henderson was so only in relative terms. Hitler still spoke of annihilating Poland.

[Kershaw, p. 316] (Hitler Biography)

When was this exactly? On 25 August 1939, in a conversation between Hitler and British ambassador Henderson. At this point, the Germans had double-crossed the British in Munich and had just signed a non-aggression pact with the Soviet Union that was (correctly) deemed highly dangerous by the western powers, particularly towards their joint protectee, Poland.

You make it sound as if the British had no reason to distrust the Germans. I think the opposite - the British had no reason NOT to distrust the Germans. Nazi Germany had gone back on its word repeatedly, had threatened peace repeatedly, had threatened British stability repeatedly. And, just for the record, I too am currently completely ignoring idealism as a driving motivator and am arguing purely from the Machiavellian standpoint of power politics. The Germans were not an ally that a British Empire could trust to maintain their loyalty and to stand by their commitments.

And that entirely ignores the question whether a power-oriented Britain would not maintain Britain's traditional "balance of power" stance and thus oppose a German-Soviet tabula rasa designed to carve up Eastern Europe to the exclusive advantage of Berlin and Moscow and the disadvantage of literally everyone else. But, as I hinted earlier, I don't like these kinds of thought experiments, because idealism is a factor in decision making, even by international statesmen.

Or did they actually care that much about democracy? [...] So what was really driving their struggle against Germany?

The British certainly used democracy and their love for various liberties as a justification for anti-German action. Churchill, in his war memoirs, cites his own press statement on the Munich Conference and the partition of Czechoslovakia as follows:

The partition of Czechoslovakia under pressure from England and France amounts to the complete surrender of the Western Democracies to the Nazi threat of force. Such a collapse will bring peace or security neither to England nor to France. On the contrary, it will place these two nations in an ever weaker and more dangerous situation. The mere neutralisation of Czechoslovakia means the liberation of twenty-five German divisions, which will threaten the Western front; in addition to which it will open up for the triumphant Nazis the road to the Black Sea. It is not Czechoslovakia alone which is menaced, but also the freedom and the democracy of all nations. The belief that security can be obtained by throwing a small State to the wolves is a fatal delusion. The war potential of Germany will increase in a short time more rapidly than it will be possible for France and Great Britain to complete the measures necessary for their defence.

[Churchill p. 273]

Now Churchill is not the reliable historical source - and he seem to take issue with the democratic flaws in communism far more often than with those in fascism -, but his liberty rhetoric is well-established as a leading motive to oppose the Germans. And, of course, Churchill himself was a huge imperialist, which he didn't see as a contradiction to being a democrat or a lover of liberty.

So, I guess this brings us neatly around back to the start of the question: Is it wise to subscribe to modern day ideas of liberty and democracy - or, in fact, cold-heated pragmatism - and apply those pictures backwards? Such self-reflection on our historical modes of thought is important. We need not condone outdated worldviews just because they're in the past, but we also must not automatically assume that everyone in the past had the philosophical or geopolitical insights that we have today.

Feel free to ask any follow up questions you might have.