Are linear feedback shift registers being generally discouraged by cryptologists?
There are many types of cryptanalytic attacks: Linear approximations, Algebraic attacks, Time-memory-data-tradeoff attacks, fault attacks.

For example you can read the survey: "Algebraic Attacks On Stream Ciphers (Survey)"

Abstract: Most stream ciphers based on linear feedback shift registers (LFSR)
are vulnerable to recent algebraic attacks. In this survey paper, we describe
generic attacks: existence of algebraic equations and fast algebraic attacks. ...

At the end you can find other relevant references.

Another good paper about fault attacks to stream ciphers is: "Fault Analysis of Stream Ciphers"

Abstract: ... Our goal in this paper is to develop general techniques which can be used to attack the standard constructions of stream ciphers based on LFSR’s, as well as more specialized techniques which can be used against specific stream ciphers such as RC4, LILI-128 and SOBERt32. While most of the schemes can be successfully attacked, we point out several interesting open problems such as an attack on FSM filtered constructions and the analysis of high Hamming weight faults in LFSR’s.

For time-memory-data tradeoffs attacks you can read: "Cryptanalytic Time/Memory/Data tradeoffs for stream ciphers".