Generally a good idea would be not to do anything that actively shows contempt for the congregation's practice (unless you really feel like you have to be an iconoclast). Stand up when they're standing, sit when they're sitting. You might want to compare, for instance, questions of a fellow whose practice differs from the congregation's with regards to tefillin on Chol HaMoed, or an Israeli visiting America on the second day of YomTov. (On the former, for instance, if everyone in the shul is wearing tefilin and one person isn't, that's not demonstrating a conflict; maybe that one person just has severe digestive problems and may need to excuse himself any minute now.)
I know of one fellow whose practice was to say Tachanun (the extra-sad prayer) who arrived at a shul that was saying Hallel (extra-happy prayer). He stood when they stood and just said his sad prayer, no one noticed what page he was on or exactly what words he was saying to himself. Meanwhile, another fellow at that shul felt like making a public statement that his opinion was to say neither the happy prayer nor the sad one; he made a very clear point of getting up from his seat and going to sit and read some Tanach for a few minutes. That generated friction with his fellow congregants -- do you really need to go there?
Otherwise, whatever your view on how to observe Israeli Independence Day in a religious manner, you'll probably have some range on what other views are "valid", which would affect how you'd behave when surrounded by others whose practice is different than yours. Many, for instance, find Hallel without a bracha, after the davening, unobjectionable as you're just saying some extra Psalms (once your formal text of prayers are over, sure say whatever Psalms you like, any day you like, why not?).