I do believe that there is indeed somewhat of a problematic attitude in the frum world towards accommodations for our particular needs. As yekke2 put it, The feeling of entitlement – that they are ?????? to give you special treatment – is an attitude that brings the most negative attention. Often, with just an apologetic smile and kind request, you can get your way without making the Chillul Hashem.
That said, I do not believe that either of the examples cited in the OP are displays of such a negative attitude. As akuperma pointed out, if the gym was only concerned about safety/insurance they could have had the lady wearing a skirt sign a waiver, or they could have banned her from certain machines.
As for the Rabbi getting the bowling alley’s TVs turned off, while I do not agree to the underlying attitude of making the whole place change to fit one’s own standards, I do not believe that going over the managers head is the chillul Hashem its being made out to be. (And apparently, the corporate office sided with the Rabbi.)
Syag Lchochma:
First, an important preemptive clarification; I do not in any way condone behavior by frum people that is condensing, nasty, disrespectful, overly demanding, etc. It is wrong, it is a chillul Hashem, and it must stop.
However, I do not believe that your comparison was an accurate one. I believe that there is a world of a difference between provoking those who hate us into actually attacking us, and engendering feeling of dislike from people who otherwise seem to have no problem at all with us. Both of them are clearly wrong, but only one of them is actually dangerous.