Anandi has been wearing a ghagra choli from her childhood. Her dress is a product of the environment she has grown up in and something she is used to and comfortable in. I have been wearing T-shirts and trousers since my childhood for the same reasons.
Shiv was raised in a city, had a university education in the UK, and works in a government post. Therefore he wears suits, and wears traditional clothing for festivals and visits to the temple. I think that is normal - I know many people of both genders who do the same (including myself). I don't think anyone should be judged for not wearing traditional clothing on a regular basis any more than they should be judged for not wearing modern clothing on a regular basis).
The problem with Saanchi is that she is, as far as I can tell, repulsed by very traditional Indian clothing which one wouldn't generally see in a city (I am assuming this attitude of hers is limited to outfits such as ghagra choli, since she obviously doesn't have a problem with her mum and aunt wearing saris or deem them 'behenji'-ish for the way they choose to dress). As Suchi and others have said, true modernity is not about being Westernised, but about being open-minded. Saanchi can choose to wear whatever she likes herself, but she's crossing the line in trying to dictate to Anandi how she should dress and implying that she is somehow a lesser person for wearing a ghagra choli.
Also, Anjana has given a great response to the "Shiv is an MCP because he's chosen the traditional girl over the modern girl" argument, but just to add - I don't think Shiv weighed the pros and cons of Anandi and Ashi in his head and consciously went for the more traditional girl. That's not how love works. Anandi embodies the qualities he wants in a life partner, and he's attracted to her. He saw Ashi as a good friend, but just didn't feel that way about her, and that's just life. They were unsuitable anyway, as Anjana's already explained really well.
That said, I was really annoyed by the movie Cocktail, in which Saif Ali Khan ended up with Diana Penty (who was playing a quiet, demure, innocent, traditional Indian girl) instead of Deepika Padukone (who was playing a very Westernised mini-skirt-clad girl who enjoyed clubbing and getting drunk). But that was because I thought that a) he was incredibly selfish in expecting Deepika to just magically be OK with him dumping her and hooking up with her best friend, b) there was no decent build-up shown as to why he and Diana were drawn to each other, so the whole thing felt contrived, and I couldn't help but feel that he blatantly had more of a connection with Deepika since they had shared interests and similar personalities, whereas he and Diana were opposites, and c) because Deepika was shown trying to be more 'Indian' in order to win Saif's heart, like there was something wrong with her being Western and she had to change in order to become 'marriage material'. Whereas the Ashi-Shiv situation in BV was totally different... a) Shiv never led her on, so there was no question of him being at fault or selfish (maybe clueless, but that's not unreasonable given that she never told him how she felt directly and he can be a bit of a bhondu sometimes, as we've witnessed xD), b) he has way more in common with Anandi than he does with Ashi in terms of their goals, interests, and life partner aspirations, and c) Ashi was never portrayed as a lesser person for being Western, just as a nice girl who liked Shiv, but whose feelings were unfortunately not reciprocated, who handled her heartbreak with admirable maturity and who will hopefully find someone more suitable in the future who will love her for who she is. She would have had to change herself and make many sacrifices to be with Shiv, so it's better than both of them end up with people with whom they fit better and around whom they can comfortably be themselves.