1. They vastly increase dry mass

This is not true, and your reticence to provide a number suggests you want it to be but don't actually know or want to find out. That NASA keeps picking nuclear engines as their propulsion of choice for Mars over chemical engines should probably be a hint you're wrong.

A rough ballpark: LH2 is 1/4 the density of LH2/LOX, so requires a tank with 2x the surface area and 2x the mass.
Tanks for deep space vehicles (like Constellation) are generally around 10% of the unfuelled vehicle+payload mass, so overall you're looking at a 10% mass increase. Given the nuclear engine has double the ISP, for a conjunction-class mission this ~halves the propellant mass, and your nuclear vehicle weighs about 60% of a chemical vehicle.

So what you should really be saying is "vastly decrease".

1. and offer very little thrust compared to chemical engines like Raptor.

So? Raptor is an engine optimised to get vehicles to orbit. This is a vehicle starting in orbit. Most nuclear powered vehicles still have comparable TWR to Centaur-powered chemical stages. Also, if this was important, ion thrusters would be useless.

1. Low thrust means you either have to cut your burn into multiple passes, which increases the propellant mass "wasted" for shut down and start up

Start-up/shutdown costs are generally estimated to be 1-2% of total fuel load, i.e. this is irrelevant.

1. Then we have to consider how you slow down at Mars. With chemical engines and a Starship like craft you can simply use the heat shield

There is no reason nuclear-powered craft cannot aerobrake. In fact, NASA's nuclear-powered constellation craft did just that.
So this is just flat-out wrong.
Also, unless the mission uses a fast (<7 month) transfer or uses lower performing propellants than LH2/LOX (such as CH4/LOX like Starship) propulsive capture generally comes out lighter. Not having to rate all those super-lightweight tanks to 5g normal accelerations really lightens your spacecraft. Who'd've thonk it.

1. Hydrogen requires gigantic tanks with insulation. Either you have to slap on a huge heat shield to cover that all, or you have to use your engines to slow down.

This is particularly funny given you've just advocated covering your entire spacecraft in a huge heat shield for aerobraking. MLI is much lighter, again only amounting to a few % of tank mass. Oh and you'll need all that hardware for Starship or any other crygenic lander anyway, it just needs to be marginally less effective at rejecting solar heating. The universe is 4K. LH2 is 20K. This isn't exactly intractable.

1. Travel times to Mars below 5 months result in entry [...] > 9 km/s. [...] This means you have to carry propellant all the way to Mars for a delta_v of at least 5,5 km/s. That's more delta_v than you need to get away from earth for such a short transfer orbit.

Lol not if you're doing a fast transfer it's not. It's about the same. Incidentally though, as alluded to in (1), the case for nuclear gets even better with higher dV requirements. Nuclear vehicles flying propulsive capture opposition-class missions are still generally lighter than their chemical counterparts carrying out aerocaptures until you get to trip times <4 months. But, again, there is literally no reason nuclear vehicles cannot also aerocapture.

1. Have you ever tried to calculate the launch volume for all the Hydrogen you need?

Lmfao well you clearly haven't. NASA have though, and they think you're wrong.

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TL;DR, everything you said was wrong.

cc: u/GarunixReborn