The answer is sometimes.

Eurostar and Thalys for example charges different rates whereas Trenitalia doesn’t. The difference though is not a huge amount in the context of your total spend on your holiday. (Eurostar is 8 euro per seat difference 38 v 30 1/2).

Much more significant is whether you are travelling in countries with optional reservations or on predominantly mandatory reservation trains (such as France). Even second class adds quite a chunk of cost, especially on cross border TGVs.

There is plenty of advice on the community to balance reservation costs.

It really all boils down to where you want to go-it differs quite a,lot between countries-plus that in some there is simply no real check at all on 1st-anyone sits and there goes your privilege! OTOH you may be sniffed on by the tipical bisnees travellers sitting on expense accounts if you are clearly a young bekpekker.

IF you are still in the junior sector: go 2nd-in the not that far past it was even impossible to buy 1st for that age.

As a traveller across Europe in 2022 in First Class we experienced none of these old fashioned prejudices. We were simply fellow passengers appreciating the size of the seats and the extra space.

Our tickets were routinely checked and second class ticket holders were always ejected or charged extra. I usually had reservations and nobody took my seat, although a couple of times our neighbours would need to play musical chairs. 

At no time were we, clearly tourists, albeit seniors, made to feel unwanted, and if anybody did I would be tempted to react. 

I agree that, irrespective of class, bad manners and behaviour can spoil everybody’s day but that is far from reserved for first class. Just the opposite in my experience, on most trains First Class was a haven of peace. The only exception was an ICE to Brussels which was overfull and second class passengers spread into First Class corridors and floors, but the majority of seats were occupied by reserved passengers.
Finally I fail to see why travellers on a youth pass should be discriminated against if they have the funds to travel first class.