Quoting RAE themselves:
[...] ese empleo tradicional de la tilde en el adverbio solo y los pronombres demostrativos [para distinguirlos, respectivamente, del adjetivo solo y de los determinantes demostrativos] no cumple el requisito fundamental que justifica el uso de la tilde diacrítica, que es el de oponer palabras tónicas o acentuadas a palabras átonas o inacentuadas formalmente idénticas, ya que tanto solo como los demostrativos son siempre palabras tónicas en cualquiera de sus funciones. Por eso, a partir de ahora se podrá prescindir de la tilde en estas formas incluso en casos de ambigüedad. La recomendación general es, pues, la de no tildar nunca estas palabras.
Bold and [annotations] mine.
Translation:
That traditional use of the accent mark in the adverb solo and demonstrative pronouns [to tell them apart from, respectively, the adjective solo and demonstrative determinants] does not fulfill the fundamental requisite that justifies the use of the diacritic accent, which is to distinguish stressed or accented words from formally identical unstressed or unaccented words, since both solo as well as the demonstratives are always stressed words in any of their usages. Because of this, from now on the accent mark may be dispensed when writing these words, even in case of ambiguity. The general recommendation, thus, is to never put an accent mark in these words.