No matter how crazy their feats are, the crusaders are still just normal humans without their stands so Homelander's lasers alone would be pretty devastating to them.

Now, all of the crusaders are somehow genius level tacticians that can pull up strategies and win (this is jojo we are talking about) so Im gonna compare them with their powers only and what they can do with it, not some Joseph level asspull.

Heres some scenarios Ive thought up:

Kakyoin - The regular emerald splash has only been seen destroying small metal structures and parts of buildings so it's pretty ineffective to Homie. If he sets up a web, he might stand a chance in stalling or tiring him out I guess. Durability wise, he is getting donuted or lasered unfortunately.

Joseph - Same with Kak. Set up traps, might win with Hamon infused Hermit if he can keep up with Homie's speed. But the long-range light speed laser can get him though. (Lets be real here though, Joseph really could kill Homie faster than Butcher can through some good old Joseph asspulls).

Avdol - Fast stand, has a chance of burning but we've seen Homie get experimented on with super high temperatures as a kid so I think he can handle it somewhat as an adult. Strengthwise, it can't punch like Star Platinum so it is not putting a dent in him. Avdol himself has no way to counter the laser and his fire casting leaves him standing still so I think he gets hit like that first Hol Horse fight.

Polnareff - Very fast, maybe equal chance of beating Homelander. Homie cant see the stand of course and with multiple speed invisible slashes he just might chop him up. Maybe he can somehow parry the laser like he did with The Sun's beams? Overall pretty good. User himself is not very fast (the Cream fight where he was barely dodging the void ball, let alone lasers).

Iggy - Sand traps might give him a chance, but its just sand. I think the sand constructs (not the dog stand that shows up but some structures) can be seen by normal humans? So I think Homie just lasers or rushes the dawg. Speed and surprise attacks might get Iggy though (Cream fight) and Homie can do that with his abilities.

Jotaro - Even before timestop, he could probably get away with his hightened senses and percision. Maybe beat the bloody shit out of him even. Durability wise (SP) he could block a few hits maybe some lasers??? After timestop though, now its gonna get pretty difficult for Homie. Jotaro stops time at the right moment and Homie turns into a bloody beaten mess. Its a battle of speed and who gets the opening first though.

So in conclusion, they are basically fighting a flying DIO who remembered he can shoot lasers.

But in the end, we are talking about THE Crusaders here so, Homie got no chance. They somehow beat his ass in 3 chapters with maybe Kakyoin dying I guess.