This is the single most consequential decision in cosmetic tube packaging and it is usually made on brand values rather than on chemistry.
What mono-material actually means
One plastic family for body, shoulder and cap, so the whole tube can go into an existing polyethylene stream rather than needing a facility that does not exist.
It is a real improvement, not a claim. What it is not is a barrier: oxygen migrates in and fragrance migrates out through the wall over months.
What a barrier layer does
EVOH or a thin aluminium foil laminated into the wall blocks that migration. Formulas with vitamin C, retinol, peroxides or a strong fragrance can need it to hold a commercially useful shelf life.
Foil gives the highest barrier and a stiffer squeeze; EVOH gives a very good barrier with a softer feel and no metallic look at the crimp.
How to decide
Ask your formulator what the oxygen sensitivity is and what shelf life you are claiming. If the formula is stable, take the recyclable tube.
If it is not, take the barrier and be straight about it in your sustainability reporting rather than quietly hoping nobody checks.
The middle ground
Higher PCR content in a barrier tube, refill formats that get used several times, and smaller fill volumes so the product is finished before it degrades.
None of those are as neat as a single claim, and all of them are more honest.