In Islam science is classified in a couple of categories fard 'ayn (obligatory for everybody) this is any knowledge one needs to know to be able to be a good Muslim and in the daily life from acts of worship to what is permissible and what is haram for example in trading if one is working in this business...
There's also fard al-Kifayah (obligatory on the Ummah) any knowledge which must be known at least by a few Muslims, so that the Ummah wouldn't rely on the knowledge of non-Muslims to use it.
And most if not all scholars say the most preferred kind of knowledge is that which is related to religious knowledge (see also Why Knowledge is often related with religion?). (See also in Ihya' 'Ulum ad-Dyn of imam al-Gahzaly)
And the most preferred one is learning the Qur'an and teaching it.
So far I have not come to the topic of pseudoscience, but from the intro above you may conclude that all knowledge which has benefit for the Ummah is important and encouraged, based on verses like (20:114):
... and say, "My Lord, increase me in knowledge.
Examples of pseudosciences which are rather encouraged
Among these knowledge types which are highly encouraged there are Medicine and what ever is connected to the topic of healing.
Therefore you will find that alternative Medicine is highly practiced and common in Muslim societies for example cupping is referred to in the sunnah, ibn Qayyim al-Jawziya ابن قيم الجوزية is one of the authors of books entitled the prophetic medicine الطب النبوي, there you may find ahadith on the use and healing with black seeds (see Did Muhammad say that black seeds can cure any disease?), olive oil (see What are the benefits of using olive oil in Islam?), honey (which is also quoted in the quran 16:68-69) etc
The prophet also said:
... Make use of medical treatment, for Allah has not made a disease without appointing a remedy for it, with the exception of one disease, namely old age. (Sunan abi Dawood)
I've even read that ibn Sina used music as a treatment (this certainly is not a scholarly evidence for it being halal). I'd say that healing by Qur'an as non-Muslims would call ruqyah is one of the so called beneficial pseudo sciences.
Examples of pseudosciences which are not encouraged
On the other hand astrology is haram based on the hadith in sunan abi Dawod, while astronomy as far as it helps calculating prayer times etc. is allowed, while psychology (according this fatwa in Arabic on islamweb #132439) is rather frowned upon due to the non-Muslim basis of the actual teachings, even if by default it has an acceptance in Islam and should only be dealt with by Muslims who are strong in their believes. As a side note -as both are not pseudosciences- philosophy and man made laws are haram to study according the same fatwa.
Also numerology is not considered as beneficial according islamweb #106263.
So basically one could conclude that any knowledge which has clear benefits for Muslims (humans in general one could say) are strongly encouraged, while anything which is rather useless or causes harm is rather prohibited.
And Allah knows best.