After getting the invitation to a party and then notification about party starting I click on atend party but the action is automatically canceled after 2 seconds. And when I click on purple party tag on town map I only get NRaas option. It is the same way when I want to visit neighboors. I can do it manually, but my sims won't do it autonomously.

I remember when I downloaded a mod for teen nanny and because it was an outdated mod My sims couldn't inspect portal. It was the same way as this. The action got canceled after 2 seconds. Is this due to NRaas or some other mod, or is this simply a bug?

Please help!

This might not be the cause but there is a bug where you can't attend parties I and several people have seen. For some stupid reason, the party thrower leaves the lot and nobody's home to let your Sim in. Your Sim can't get in so the action is cancelled. Is anybody home? Can you not go to any parties at all? I don't know for a fact if this bug effects the typical house parties but I do know this bug definitely effects the party types introduced in University Life. I wonder what happens if you have HomeOpener when you attend one of these bugged parties? I haven't seen this bug since I uninstalled University Life so I haven't been able to test it.

I think that It is because of the Home Opener. I get only NRaas option whenever I try to enter a house or a party. And I was wrong about the canceling action. The "attend party" interaction, for some reason, actually doesn't exists.

It very well might be what is causing the problem. HomeOpener's function is to force the game to display the interior contents of every lot in town by allowing your sim to be automatically greeted on all lots and can stroll through any door anywhere in town. Try removing HO, clear your caches and see if that relieves the problem.
If that does not work try using Master Controller to:
Reset your town and/or
Check for social jigs and flush them .. those have been known to cause actions to be cancelled.