Westerners who are not Dvijas and are probably not Hindus have done yeoman service in translating Vedas and other scripture into English.
The prohibition against writing down scripture has universally broken down and everything is available everybody, Hindus (regardless of caste) and Non-Hindus at the click of a button sitting at home, whether bathed and in ritually clean status or not.
Does scripture talk about the ill-effects, if any, from such universal dissemination of scripture?
According to Atri Smriti, if a Sudra recites the Vedas, then that brings about the destruction of the whole kingdom.
By following his own religion even a S'udra enjoys the celestial region. Another's religion should be renounced like the most beautiful wife of another person. (18)
The S'udra, who engages in the recitation [of the Gayatri] and the offering of oblations to the Sacred Fire, should be killed by the king ; for by that he becomes the destroyer of the kingdom as the water is of fire. (19)
Acceptance of gifts, giving instructions [in the Vedas] selling an article which should not be sold, and officiating as a priest at a sacrifice the doing of these four, [is described] in the Smritis as outcasting the Kshatriya and the Vaisya. (20)
Although translator added "of the Gayatri" in the brackets but I think it is talking about reciting the Vedas.
Will there be ill-effects from universally disseminating scripture to non-Dvijas?
By "scripture" I assume you mean Vedas. If so, it can lead to national disasters, but Smritis can be disseminated to everyone including non-Dvijas.
In the Ramayana, a Shudra was doing Vedic tapasya, which caused the death of a Brahmana's son. So, Rama being the king, had to protect Dharma and punish Adharma, and so he executed the Shudra. The Shudra was re-born as a Brahmana.
However, non-Dvijas are permitted, and encouraged, to do Agamic/Tantric/Smarta tapasya. For example, Sri Vaishnava non-Dvijas chant a particular mantra from the Pancharatra Agamas.
Scriptures does not necessarily mean the vedas.There is no bar in teaching Ramayana, Mahabharata or the Smrities or Puranas which are also scriptures.
One reason of writing the Puranas is the very fact that "stri-sudra-dwijavandhunaam trayi na srutigochara" ie The Vedas can not be heard by the women, sudras and fallen tri-varnas.
So except Srutis, all are expected to be able to learn other scriptures.
Sri Sitaramdas Omkarnathji points out that these scriptures should be read under supervision of a guru (ie not to be read on own),as that is our tradition.(Ref: M-kar Baba, Sitaramdas Omkarnath, Mahamilan Math, page 2).
Without proper knowledge of Sanskrit and our tradition and culture, teaching or Learning of the above books are like teaching or learning English poetries and dramas without knowing english.
"Their true meanings can not be understood otherwise.(Ibid page 2).
So neither bad nor good effects will be the result.It will just be a wastage of time of all involved.
As Sitaramdas Omkarnathji points out:
Without proper tapasya, one can not understand the real meaning of the Sastras.(Omkarnath Rachanavali, Sitaramdas Omkarnath,Vol.7,page 1).Max Muller and Ramesh Dutta etc who have traslated the Vedas have seen only the skeleton of the Vedas and eaten the bones of the Vedas.(Ibid, page 97-8).
