The main reason is that in the HP world politicians (both magical and muggle) are incompetent and easily controlled, and they seldom take resolute action so they don't pose real danger.
They characterized as opportunistic people who make populistic decisions to appear good in their electors eyes creating the impression that they actually doing everything to promote the welfare and safety of their people, while in fact they are mostly interested in keeping their positions, devoting most of their efforts and time to machinations
to conceal how ineffective they are
to ensure they stay in power.
HP politicians also often blindly follow buerocratic procedures without inquiring as for the reason for it. For example, Fudge informing the PM about the dangerous creatures brought to the UK:
“Oh, and I almost forgot,” Fudge had added. “We’re importing three
foreign dragons and a sphinx for the Triwizard Tournament, quite
routine, but the Department for the Regulation and Control of Magical
Creatures tells me that it’s down in the rule book that we have to
notify you if we’re bringing highly dangerous creatures into the
country.” “I—what—dragons?” spluttered the Prime Minister. “Yes,
three,” said Fudge. “And a sphinx. Well, good day to you.” ~HBP - The Other Minister
Now I ask you, what was the point informing the PM in this case? Fudge did not wait for the PM's approval, did not give any details about the logistic, timeframe, location and possible dangers entailed. What was the PM supposed to do with the information? Fudge was just following the regulations to the letter and the muggle PM accepting it without any objection.
To be fair, the open channel of communication between the ministers is useful when needing muggle assistence, for example catching Sirius Black:
“That man!” Harry said, forgetting his troubles for a moment. “He was
on the Muggle news!” Stan turned to the front page and chuckled.
“Sirius Black,” he said, nodding. “’Course ’e was on the Muggle news,
Neville, where you been?”
Harry Potter and the Prisoner of Azkaban - The Knight Bus
Ensuring the muggle PM's accistance is actually helpful - after all, the muggle PM has access to mass media, resources, manpower to mobilize or to evacuate an area if needed.
Even better, the PM could have been of assistance in the offensive war effort against Voldemort's armies, but it seems the idea (or any other helful idea really) never occured to Fudge.
Fudge himself apperently thought that the risk exposing the magic community is negligible as the information is too unbelievable to share::
it the best way to maintain secrecy.” “But then,” bleated the Prime
Minister, “why hasn’t a former Prime Minister warned me—?” At this,
Fudge had actually laughed. “My dear Prime Minister, are you ever
going to tell anybody?” Still chortling, Fudge had thrown some powder
into the fireplace, stepped into the emerald flames, and vanished with
a whooshing sound.
The argument of the PM keeping silent else being ridiculed and doubted doesn't stand. At least not in the real world. Only someone as unimaginative and dim as Fudge could have thought that it would prevent a determined and resolute person who is reasonably intelligent from acting, especially if such an individual would have preceived the magic community as a threat or view them as an asset to be exploited. At the very least, he'd try to subtly conduct research on the 'wizards' collecting as much information as possible. After all in the real world PMs have secret services and research facilities at their disposal to investigate 'paranormal activities'. The PM could have initiated a project Toran Darel II style. It should have been be doubly true when there was an actual threat to life and property, with Voldy's people running amok.
Fudge even gave the PM opportunity to capture a test subject when he exposed his inside man posing as a secretary (Kingsley) to the PM.
What would have prevented a real life PM to order the SIS to treat Kingsley as an extremely dangerous foreign spy / terrorist and capture him, using the best agents (as in slip him some sedative in his morning tea or take him out with use some nerve poison gas or employ a sniper to shot him up from afar with some anesthetic medication), then quietly take him to some secure research facility and question him?
A sedated and bound wizard without his wand can be a valuable source of information, and in the situation the PM found himself at the beginning of the HBP he needed information about those mutant freaks with paranormal abilities like he needed breathing.
After all, it seems said freaks at the time of the events in HBP were spit into two fractions engaging in a civil war which also threatened the lives of civilians - the members of the psychotic fraction were completely out of control, committing mass murders and destroying bridges and buildings just for the fun of it, while the more sane fraction tried to stop them, but apperently was doing a pretty sucky job at it.
In a functioning government the PM would've thought of crisis management and the need to collect as much data as possible from the captured paranormal using the best neurologists on government payroll to check the freak's brain scans, radiowave composition and such to expose possible vulnerabilities or to find a way to build shields against magic energy waves (or whatever those creatures doing with their brains when they destroy bridges or slaughter old ladies in their homes with their freakish mental power and their channelling devices called 'wands'.)
The next rational step would have been to share the information with as much high ranking army/navy/intelligence officers with high clearance as possible so the so called 'wizards' couldn't take them all out, then negotiate with those 'magic ministry' freaks with bad fashion choices from a position of power, offer them a truce and alliance against the psychotic fraction, combine magic and technology to take the psychotic fraction out, then conduct even more in depth experiments to harness the magic power to use it for the 'good of humanity' (that is, to make weapons).
But luckily for Fudge in the HP world
the muggle PM in HBP (and his predecessors) had the similar cognitive skills as the wizard politicians, therefore he did not pose any danger whatsoever.