Where to start with that?!
Starting from the beginning of the Modern Age (or even earlier), Europeans have been considering time as linear; time has been compared to an arrow flying from the past via the present to the future.
This is not really a 'European' thing. The linear conception of time can be very loosely associated with the Abrahamic eschatological idea of a movement towards a future point commonly identified as the 'end of the world'. As such, it's common throughout the Middle East and the Muslim world more widely. Note that this is a mythological conception rather than a linguistic one.
This is reflected in all European languages
Not true by any means.
If you're going to generalise this, I think you can say that (I need to check the evidence) Indo-European cultures have a
front-back conception of time, where the future is forward ahead of you and the past is back, behind you. These conceptions are revealed not by the tense/aspect systems of language but rather by the
metaphors people live by.
which, accordingly, have three different forms of verbs (tenses).
Well, no. As we've established, neither German nor English has a future tense, for example, both being very closely related linguistically as West Germanic by family. This is a feature of the Germanic family of languages more broadly, as far as I know.
However, some Oriental cultures envisage time as cyclic, and then moving into the future ultimately brings you back to the starting point.
That's correct. Indic cultures too.
This worldview influences Asian languages that may have no future verbal forms.
I think that's probably the case, yes. I do think that language is influenced by worldview, yes, but it's also a little the other way round, like a feedback loop.
A trend that has relatively recently started to develop in some European languages is based on avoiding future tenses/forms of verbs.
Example? Evidence?
This clearly manifests itself in German where the future-indicating auxiliary verb werden (routinely put before an infinitive) is being increasingly omitted by most speakers, especially in an informal setting.
That's interesting. Can you give me an example of this, so I know what you're talking about?
Is the West becoming increasingly Orientalized? Will it also consider time as cyclic?
No. Why would it?
My view, in a nutshell, is that conceptions of time come primarily from the way the human body interacts with its surroundings, and then are modified and reinforced by the stories/myths that we tell ourselves.