The US has a doctrine "the fruit of the poison tree"
"Are law enforcement officers permitted to commit other felonies whilst in pursuit of a larger crime?"
The final arbiter here, is the courts. If they allow evidence which has been illegally obtained to be presented, then the assumption is, it's "allowed". If they do not allow illegally obtained evidence, then it's not allowed.
The US has a doctrine "the fruit of the poison tree" which is a principle that illegally obtained evidence - and subsequent discoveries - are not permitted. It's a frequent plot device in shows like "Law & Order", and quite fascinating to a UKain, as there's quite a body of precedent and law around it (for example a cop is permitted to search an arrested suspect, but *only* to ensure his own safety (i.e. no hidden weapons).
Here in the UK, 99% of courts (i.e judges) have repeated made it clear they couldn't give a toss what laws may have been broken to bring a case to court. The (somewhat specious) reasoning being that to punish the state for breaking the rules would deny the individual victim in the case justice. Or, in other words (but not ones they'd like, no matter how accurate) "the end justifies the means". Personally, I subscribe to an old-fashioned notion that the law applies to all. But I know that's not really the vogue now.
UK cases where a judge has thrown out dodgy evidence are far and few between, and therefore newsworthy, The last one I can remember (so showing my age, and how shit the system is) is when the judge in the Colin Stagg trial went ballistic at the prosecutions use of tabloid-style psychobabble, and tore the CPS and Met Police a new one - very publicly.