Fred Sturm is absolutely right. The historical literature leaves no room for doubt that equal temperament was universally prescribed in 19th century German literature on piano and organ tuning, music theory, composition, and acoustics. ET had already essential become the recommended temperament from about 1750 onwards, although undoubtedly some continued to prefer slight differences in key color. However, as the century draws to a close, references to such a preference become increasingly rare, and ET is ever more roundly praised as being the most perfect of all temperaments. That's not including Kirnberger, of course, whose crude Just/Pythagorean mix was so far outside of the mainstream of prevailing theory and practice that it cannot be considered anything other than an historical curiosity, which as Marpurg said, was "praised by many, used by no one".
In terms of actual practice, it's quite likely that many musicians/tuners continued to use slightly unequal circulating temperaments up through the first decades of the 19th century, either by choice or by accident, but by the times of Brahms birth, ET would have been expected of any competent tuner, even if were imperfectly implemented. Even with Sorge's method (c. 1750), if you are careful and demanding, you can get so close that any deviation is musically inconsequential, especially if you use a well-constructed monochord as guidance, as he recommended. Any technical limitation in terms of implementation disappears completely with the publication of Scheibler's method in 1834. With the various further explications and elaborations published soon thereafter, most notably those of Loehr (1836) and Töpfer (1842), it became quite easy to tune an absolutely-perfect ET, even without the aide of Scheibler's forks. His methodology was referred to and highly-praised over and over again in all manner of subsequent publications, such as articles in the AMZ, books on acoustics, piano making, etc, so any German tuner during the second half of the 19th c. who didn't know about it would have simply been incompetent.
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Paul Poletti
Builder/restorer historic keyboard instruments
Poletti Pianos
Barcelona