A conservative philosophy was one that sought to promote and to preserve traditional practices. It could also refer to underestimating a numerical figure.
In 2268, R.M. Merik described 892-IV as "an ordered world...a conservative world based on time-honored Roman strengths and virtues." (TOS: "Bread and Circuses")
In 2293, Spock advised taking Gorkon's side "lest more conservative elements persuade his Empire that it is better to attempt a military solution and die fighting." (Star Trek VI: The Undiscovered Country)
Captain Montgomery Scott told Geordi La Forge that a good engineer "is always a wee bit conservative on paper." (TNG: "Relics")
In 2369, Farallon admitted that he had moved too quickly on development of exocomps and that he "lack(ed) that conservative streak most scientists have". (TNG: "The Quality of Life")
In 2370, Ro Laren noted that Maquis she'd met tended to be more conservative. (TNG: "Preemptive Strike")
During Captain Carol Freeman's trial for her alleged involvement with the destruction of Pakled Planet, Ensign Brad Boimler told Beckett Mariner that he had very detailed log entries.
Upon realizing this, Mariner realized that all they had to do was compare his PADD with what she was accused of to show there's a contradiction, meaning she's innocent. Mariner then excitingly said "Take that, conservative military court!" (LD: "Grounded")