Is "保守" considered derogatory in Chinese? In English, the word "conservative" seems neutral. However, the Chinese word "保守" seems to carry a negative connotation (Am I right)? What word should I use if I would like to express the english word "conservative" in a neutral way? How about in a positive way?
From the stand point of innovative and liberal thinkers, 保守思想 (conservative thinking) does carry a negative connotation of inability to adapt 

For example: 思想保守的人不願譲子女與外國人通婚 (conservative thinking people do not want their children to marry foreigners) . Since most people nowadays do not mind international marriage, the ones who oppose it had became the minority.

You can say 保守思想(conservative thinking) is polite words for 陳舊思想(old thinking) or 落伍思想 (outdated thinking) 

But 保守 as an adjective or adverb on it's own is neutral

For example: 保守估計 (conservative estimate); 保守作風 (conservative style); 保守(地)估計 (conservatively estimate)


  How about in a positive way?


You can replace 保守 with 穩建 (cautious) which implies "careful" and "steady" or 慬慎 (cautious)

Example: 作風穩建; 立場慬慎