Your original question/premise was that "many" (unnamed) complain that Obama has committed numerous unconstitutional acts, so you want to know what "rights" have been taken away.
First, I have no idea precisely what the "many" have claimed. However, in a previous thread (in which I described Obama as average or above average, as I recall) I pointed out my two main concerns about the Obama presidency.
First, we had a dumpster fire of a system for paying for healthcare in this country before he took office. I personally believe all the ACA did was pour gas on that fire, as opposed to solving any real problems for any appreciable length of time (I don't believe temporarily adding people to the list of insureds, only to see them be forced off, with others, in the next couple of years because of outrageous premium prices is really an improvement.)
Second, I think Obama's practice of "if Congress won't act, I will" sets a dangerous precedent and is arguably unconstitutional. Another example beyond the aforementioned immigration action includes some appointments of judges under the NLRA which were later set aside as being unlawful. There were also some portions of the ACA that were legislated that certain things had to be done by certain times, and when it became politically expedient to shift those deadlines, he did so unilaterally without Congress, who really has to do the legislating.
His acts weren't so brazen as taking peoples guns away, declaring that certain segments of society no longer have the right to marry, or that type of thing. But I don't know that anyone has actually accused him of doing those things, although some may have accused him of wanting to do certain acts.
My concern about the Obama acts that I delineated is not so much the immediate impact on our "constitutional rights" but a slow erosion of some of the protections our form of government has had in place to prevent rule by dictatorship. Every president would love the authority to just declare what the law is. To the extent that any president chips away at that limitation, it is ultimately a bad thing.
