When Barry or Arin say the same lines Suzy says, people suddenly find it funny.
When Suzy points something out that people complained about (like how Arin repeatedly overlooks this and that), nothing in the spiteful comments changes, wheras if Barry or any other grump for that matter - had pointed it out, the top-comment would be something like; "Praise grump for finally telling Arin about whatever complaint you had."
If Suzy does it, hate prevails.
If Suzy makes the most jokes among the grumps in an episode, hate prevails.
If Suzy is in any video to begin with, hate prevails.
Many comments are offences on how Suzy looks like - she is the only grump who's ever attacked for their looks - and that on a huge scale.
If you've ever been a girl, you'll know from experience that people will be very on the edge about how you look like, and what you wear.
If you don't dress or look the way others want you to; insults and offences galore.
Sexism is definitely part of the hate, but a lot of people just don't realize that. And hate on everyone who dares to point it out to them.
If you legitimately find a grump not funny, and it isn't Suzy - then you wouldn't hate on them this way.
Whenever I saw comments about how people found Barry not a funny grump when he started out (and he really wasn't imo.) - they were very tame. They were like, "I love Barry, but he kinda isn't as funny as Arin or Ross imo."
None of them are even remotely close to being as offensive as any comment about Suzy.
"We hate on Suzy 'cause she isn't funny, not because she is a woman." is a bad excuse, when you're basically saying;
"we're telling you to die and get cancer, how you're ugly and a disgrace - because we don't think you're funny."
It doesn't even matter about this being sexist, that kind of hateful behaviour in itself - is already fucked up. Like, no. None of that would justify you saying such terrible things to a person.
TL;DR
Sexism is a part of it, but even if it wasn't - the hate is messed up.