There are no Dudhsagar falls between Lonavala and Karjat. The Braganza route's challenges are different compared to those of the Bhor ghat route.

What these people are afraid of, is actually a fear shared by many outsiders too.

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the part where the railway tracks cross the falls, there is a severe space constraint. The track crosses the first level of the waterfall very close to a sudden drop. It will be extremely difficult to construct another bridge there without constructing some kind of earthwork to strengthen the area and provide a stable foundation for the bridge. This will most likely end up altering the waterfall area significantly, probably even eliminate the 2nd drop of the waterfall completely by providing some other safe channel for the water to flow.

As most rail fans would know, the Dudhsagar falls and the railway bridge crossing them, are well known to tourists and the location is quite famous. Any altering the falls can potentially ruin the beauty of this place and detract tourists.

First of all Railways are the most economical mode of transportation in the country especially the freight traffic. Doubling of tracks will definately be helpful economically which is the need of the hour now in Goa. After the ban on mining in Goa the economy has suffered badly and due to which many people depended on mining and related sectors lost their jobs and businesses.
And this is not the only project that is opposed people are also opposing the widening of NH4A highway, IIT project, Mopa Airport, restating of mining, etc. and on the other hand the same people are hammering the government night and day for not providing jobs and the falling economy.
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doubling is cleared by both Goa and Karnataka forest departments and I don't think adding a second line on the already existing route would damage natural beauty.
Moreover now due to lack of jobs or good salaries many Goans are moving to other countries I can name atleast 100 people who I know working in Golf, UK or on cruises I myself am personally trying past two years for a job at UAE as it's difficult to sustain a decent life in Goa.
These people opposing also are supported by a group called Revolutionary Goans which is utterly racist they call all non Goans as "Ghatis" means one coming from the Ghats and sorry for saying it's you also as per them, that group's main motto is to form a regional party through which they can enter politics and they are all around doing selective outrages in which some migrants are doing some misdeeds or criminal activities and portraying an image to Goans that migrants are bad and need to be kicked out of the state of Goa and whole Goa belongs to Goans only so it's natural that when people are brainwashed by such ideas they will oppose any kind of development project as it will definitely bring in more migrants due to the growing economic activities.
In the end I would say it's more political especially regional politics and attitude of some Goans towards non Goans that people are opposing any kind of development projects without realising that it would be Goa which would suffer ultimately.
All this is coming from myself who is a native Goan.