陈 and 旧 were not derogatory in Old Chinese. But “陈旧” is a slightly derogatory to derogatory term in many modern Chinese usages.
The entry for “陈旧” in 《重編國語辭典修訂本》 says this:
陳舊:過時而不合時宜。(dated and antiquated)
思想陳舊的人,常被稱為今之古人。People with old-fashioned ideas are often referred to as the ancient people of today. (derogatory)
In 《现代汉语词典》 the entry for 陈旧 says this:
陈旧:旧的;过时的。(old; dated)
设备虽然有点儿陈旧,但还能使用。The equipment is a bit old, but still works. (slightly derogatory)
陈旧的观念应该被抛弃。Old-fashioned ideas should be discarded. (derogatory)
A random comment on an online bookstore says:
知识有些陈旧,但是书真的很好。 The knowledge is a bit outdated, but the book is really good. (derogatory)
There is a medical term called
陈旧性肺结核 Obsolete Tuberculosis. (neutral)
Other examples:
Derogatory:
(他)抱怨倫敦的地鐵非常陳舊。
看法总是要陈旧过时,而事实永远不会陈旧过时。
家俱陳設實在陳舊不堪。
她使用的詞語未免太陳舊了。
德国总理默克尔周三警告俄罗斯不要重新陷入关于势力范围的“陈旧思维模式”。
不落俗套,摆脱陈旧感!
言辞也许陈旧,情意不曾偏离。
两个州选区居民各自面对不同的民生问题,包括水灾、道路、沟渠、杂草、基建陈旧、牛只游荡等。
厂领导终于抛弃陈旧观念,开始引进新的生产技术。
宇宙和社会是那么陈旧,无味,虽则它们其实比‘儿时’新鲜得多了。
那新摆出来的烧饼,更是陈旧不堪,暗想这种烧饼,还有什么人要买呢。
这些规章既陈旧又不现实。
Neutral:
陳舊性瘀血
Hence it is derogatory in most common usages. There do exist a few exceptions, mostly academic terms.