I would definitely be challenging the new HT's uniform policy on long hair for boys - either it is a H&S issue for all pupils or for none - and I doubt he'd get anywhere if he tried to make all the girls cut their hair! It would be entirely reasonable to insist that all pupils with long hair tie it back.
On the blazers issue - whilst I do think that blazers look smart, I have had children at schools that insisted on blazers and at schools where they were optional - and the latter was far more sensible and practical, imo!
When we moved from Essex to Scotland, ds1 and ds2 were both at senior schools that demanded blazers as part of the uniform - different schools (their choice, because the different schools suited them). For a start, the blazers were pretty expensive - ds2's blazer was £36 - I remember the price to this day, because, less than a term into Year 7, dh managed to brand a huge iron mark on the front of his blazer and we had to replace it just before Christmas!
Secondly, whilst ds2's blazer was washable and tumble-dry-able, ds1's was dry clean only - which was a complete pain, when it got dirty!
At the dses new, Scottish school, the uniform rules were more flexible - they could wear blazers if they chose to (but generally it was just the prefects and some of the other top year pupils who did), and the other option was a black v-necked jumper, or fleece or cardigan - it had to open at the neck to show the tie, and hoodies were not allowed - other than that, any plain black top was OK.
It was easier on cost grounds - it was much cheaper to buy a black fleece or jumper than to buy a blazer - and more practical too, because they could each have a couple of tops, so when one got dirty, they had another to wear - and finally, the tops could be easily and quickly laundered and dried, if they got dirty.
The dses' Essex schools were very much of the 'Smart uniform raises expectations and attainment' school of thought - and both were grammar schools - whereas their Scottish school was a comprehensive - but it was 7th overall in Scotland, judged on results, the year we moved here - which, to me, proves that a more flexible dress code doesn't cause standards to drop.