Remember, the police are not a heavily armed military force. They have neither the training nor equipment to handle an active shooter situation beyond the level of a random madman with a gun. Even the elite door kicker units that go out to arrest organized crime and such at best have light body armor and the occasional MP5. So something like an organized cult raid or god forbid an actual alien assault is going to be hilariously out of their league.
Depends on the country. E.g. US and especially Russia are heavily militarised (less so now that they need everything at the front), even if their training isn't quite military, just 'cops with big guns and armoured vehicles'.
Many countries also have high-tier national counter-terror units, be they police or military. These fellows don't end at MP5-s. Heck, even bigger municipal SWAT units come with shields (on wheels), body armour, sniper rifles, assault rifles (I guess there were more SMGs back in the 90s), EOD gear and specialists, drones/robots, flashbangs, tear gas, what have you.
Of course, they are not the military at large, and in a straight shootout even the best CT unit is going to lose to a competent infantry force of similar size. Because infantry does not care about limiting damage to civilians and their environment, so no amount of room-clearing finesse or precision shooting is going to stand up to grenades thrown around like candy, mortars, machine guns and people expecting artillety to land on their heads and not staying put.
And they aren't likely to get all these officers and their gear in place before they realise it's not going to do them much good against plasma guns and super-alloy hulls, or someone manages to get some actual military on the scene, or X-Com arrives to save the day (or more likely the night
). Although the general confusion might see quite a few regular police officers turning up on the scene and into green goo before they figure out this is not a good idea.
Cultist are in a weird place where they have some military hardware but not the training. I'd expect a good SWAT unit to perform well enough against Dagonites, Exalt, even Black Lotus. The Red Dawn are where I'd draw the line of needing the actual military to contain them.
And, yeah, an alien assault is an OCP to even elite units. There is going to be a lot of confusion and panic as the enemy is something completely unexpected, never mind the plasma guns that vaporised the guy two meters to the left.