In WWII, why did multiple countries trust Nazi Germany to respect their neutrality?

I'm only familiar with the case of the Netherlands, but here your premise is clearly not supported by the facts. I'll just go over some of these briefly:

The Netherlands essentially started re-arming in 1936, but was hampered by the fact that it had suffered badly from the Great Depression, had only a small domestic armaments industry and factories abroad were fulfilling orders for their own governments. Nevertheless, the Dutch army did acquire new weapons, most notably more anti-aircraft artillery and fighter and bomber aircraft (AAA proved to be particularly useful; the Dutch destroyed some 220 Ju-52 transport planes and put another ~150 out of commission for months in repelling the initial German airborne attacks.). That the military wasn't built up "seriously" therefore wasn't a consequence of not wanting to provoke the Nazis, but of the practical problems of where to buy weapons and how to pay for them.
The Dutch Army mobilized on 28 august 1939 in response to the Poland crisis, and reservists and conscripts were called up, giving the Dutch army a nominal strength of 280,000 soldiers in a population of 9 million. The Dutch army stayed mobilized until the German invasion.
Dutch military strategy in this time was fully based on the expectation that Germany would attack; the chief aim was to hold out in a defensive line until help from the French and the Belgians could arrive.
To this end, the new supreme commander of the Dutch military, General Winkelman, on his appointment in February 1940 ordered the strengthening of the Grebbe defensive line, thoiugh sadly this work wasn't completed by May when the Germans came.
Perhaps most importantly, the Dutch had intelligence sent to them from officers in the German High Command and were aware of the German invasion plans. The invasion was delayed several times, but Dutch historians found that each time the Army was put on full alert in preparation.

Now it is true that all these efforts were in vain, mainly because the army had serious problem of command & control, communications and intelligence, as well as having poorly-trained, equipped, and motivated troops (a result of conscripting many young married men). Moreover, the Netherlands did fail to restrict the movement of Germans in the Neterlands in order to avoid provoking the Nazis, as a result of which the Germans had very good intelligence about Dutch defensive dispositions. And all this contributed to the relatively quick defeat of the Netherlands (even though the Dutch Army fought hard in many places, and suffered 2,200 dead and 2,700 wounded in casualties). But the idea that the Netherlands was quickly overrun as a result of its naivety (naïvete?) is certainly false.

Primary source on this:H. Amersfoort and P. Kamphuis, May 1940. The Battle for the Netherlands Koninklijke Brill 2010.

The short answer is that the small neutral powers of Europe (the USSR is a different kettle of fish I'll go into below) emphatically did not trust the Third Reich to respect their territorial integrity. However acknowledgement of this reality did not erase the significant strategic dilemmas that these small powers faced during the war.

One of the biggest problems facing these states was the explosive growth both the complexity and cost of military armaments in the interwar period. Not only were military arms expensive, but they also required a large and sophisticated industrial establishment to produce the numbers needed to wage a modern war. There were two basic options available for the small powers, they could form their own industry or acquire armaments from the larger, more advanced powers.

The story of Polish aviation is an example of a smaller power following the former strategy. Although Poland had cultivated extensive contacts with French aviation firms, there was a decision in the early 1930s to develop an indigenous aviation firm, PZL and create a modern air force. Although the Polish government decreed that its aircraft were to be Polish-made and designed, PZL was dependent upon the foreign expertise for advanced components like engines and propellers which had to be license-built by PZL. This added to the costs of PZL's aircraft and hampered the attempt to craft a strong air arm. The result was that the Polish government had to fund this air arm through a series of loans, support from its French ally, and selling PZL aircraft to other countries for hard currency. Yet for all of this effort, the Polish air arm was largely obsolescent by 1939. It had a modern medium bomber entering service, the PZL 37 Los, and a decent light bomber, but its mainline fighters, the PZL 11 and 7, were not as competitive compared to Germany's. The Poles hastily tried to acquire American aircraft in July 1939, but the deal fell through for a lack of hard currency. Moreover, the Poles appealed to both the British and the French to send them modern aircraft in the summer of 1939, but both nations balked at doing so because they themselves were trying to rearm and reequip their own air arms. The result of this drive for an indigenous air arm was that in 1939 the Polish had a modern bomber it could not afford to field in appreciable numbers, and a fighter arm that neither had the numbers nor the sophistication to meet the Luftwaffe on even terms. Polish aircraft designs were actually not that bad, but the structural limits of the Polish economy meant that any indigenous design was going to suffer from a protracted development cycle which was dangerous in a time of intensive technological development. A similiar pattern also emerged with both the Dutch and Czechoslovakian aviation arms; they developed their own designs but not in the numbers needed or in a timely fashion.

While the case of Polish aviation illustrates the difficulty of an indigenous defense industry, the other alternative, buying armaments from the great powers, was equally impractical for many of the small powers. A big part of the problem was that armaments often had to be paid for in either hard currency or through loans. This form of defense procurement typically is a political hot potato, but was doubly so during the global Depression of the 1930s. Many of the smaller powers saw a decided downturn in tax revenue and popular calls for the government to tighten the purse strings. The Belgian Ministry of Defense had to fight battles throughout the 1930s to implement modernization of its fortification system which meant accepting cuts in other areas such as its army size, wages, and non-combatant branches of the military. Other small state militaries also had to prioritize their investments in new military hardware which entailed having to have domestic political support. Therefore defensive armaments like anti-aircraft guns received more priority than offensive weapons like tanks. Buying foreign military equipment was also often an unpopular move during a massive economic downturn, but also one that was prohibitively expensive to do on a wide scale. This dilemma of rearmament was further sharpened by the fact that the great powers most willing to sell armaments were the ones that were the most aggressive. Both Germany and Italy's rearmament rested on precarious financing and selling military equipment was one way to inject their economies with much needed hard currency. But buying from these powers meant that not only were the smaller states now dependent upon both Germany and Italy for spare parts and technical support, but also they were helping to feed the aggressive expansion that fueled this desire for rearmament in the first place.

It was no surprise that many of the smaller powers favored collective defense over a costly solo rearmament. In the 1920s, many of the small powers placed a lot of stock into the League of Nations and the Kellogg-Briand Pact as a means to guarantee their future sovereignty and foster a spirit of disarmament. The collapse of this system of collective security in the 1930s left many of these small powers in the lurch. There were some attempts in the 1930s to form a collective security among the small powers. The Oslo Agreement of 1930 between Belgium, the Netherlands, Luxembourg, Denmark, Sweden and Norway was one such example. Initially founded to alleviate the impact of the Great Depression, the Oslo Group shifted from an economic partnership to one more preoccupied with security concerns in the aftermath of the Italian invasion of Ethiopia. But the diverse nature of the Oslo states meant that they could accomplish very little. A formal military alliance with either Britain or France was another, more realistic, option for the small states but this too faltered. Part of the problem with allying with one of the great powers for these small states was that it meant surrendering a good deal of independence and hitching their foreign policy to that of their patron. This made an alliance a highly contentious issue in domestic politics. Such was part of the problem that contributed to the dissolution of the Franco-Belgian Accord of 1920 in 1936. The Franco-Soviet Pact of the previous year greatly alarmed Belgian Catholic conservatives and other anti-communist nationalists and made it impossible for van Zeeland's coalition government to continue to sanction this alliance. Although Franco-Belgian military planning continued after 1936, it was on a semi-covert level and only between upper-echelon officers and intelligence officers lest it further weaken the Belgian government. This clumsy arrangement led to what became later known as the grave malentendu franco-belge (very grave Franco-Belgian misunderstanding) in 1940 when both the French and the Belgians believed that the other was responsible for the defense of the Ardennes thus leaving a critical vacuum for the Germans to exploit in their invasion.

While Belgium illustrated the dilemma of military cooperation, other small powers sought to feed the wolf through supplying Germany with much needed raw materials and equipment. While this seems short-sighted, there was a method to this madness. The German economy desperately needed strategic raw materials like chromium to function and any interruption of this supply threatened to deeply cut into German production. Since Germany also had a shortage of hard currency, they increasingly had to pay for these strategic minerals with advanced weaponry. This strategy worked reasonably well for both Switzerland and Turkey who fed the wolf, but also managed to acquire modern German weaponry in exchange. But both of these countries also had the benefit of geography working in their favor, which further diminished the German appetite for invasion. This strategy itself was not without precedent either. During the First World War, neutrals in the rim states opted to favor one belligerent over another as a means to guarantee neutrality and national sovereignty. The scale of the Third Reich's ambitions, as well as the string of successes in 1940-41, meant that these neutrals had to make it strategically beneficial for Germany to respect their neutrality. This was a difficult undertaking, especially since very few of the neutrals expected Germany to succeed so quickly in 1940 (even the Germans military leadership was surprised by the fall of France).

So while many of the smaller states realized that the Third Reich posed a clear problem for national security, there was little they could actually do about this threat. Rearmament was politically risky, but also an investment that might not pan out depending upon the timing of when the smaller states rearmed. Nor was an expensive rearmament a guarantee that their military would triumph in a German invasion. Poland, the Netherlands, and Belgium all mobilized to meet the German threat, but the nature of German military operations, which were often front-loaded for maximum effect, meant that such efforts could be in vain.