That's also not mutually exclusive. You can have a problem with cheap, unskilled labour from Hungary but not German surgeons. You can have a problem with skilled plumbers and brickies lowering wages for working class British workers who've done years of apprenticeships, and not Canadian bankers. You can also recognise that young families - wherever they are - inevitably cost a country more (due to schooling, higher use of public services etc) than an older person with a second property who probably spends most of their time drinking sangria and eating gambas pil-pil, inflating the local economy.
There are multiple different types of immigration, and more importantly these different types affect different people in different ways and a failure by those of us who "campaigned" for Remain to recognise this is why simply saying "Look at this tax and spend document, it shows how immigration is good!" obviously failed to resonate. So many of the benefits to immigration are felt primarily by the middle classes and businesses (who get cheaper services and employees respectively, as well as the ability to move all over Europe for good jobs and the ability to hire higher skilled workers from across the EU, again respectively), where as unskilled, uneducated workers see the value of their labour diminish amidst a growth in the labour market, are very unlikely to get job offers from around the EU and the places they live are unlikely to get wealthy foreign visitors buy a second home there to enjoy their holidays in. You don't need to convince me that immigration's been good for the UK, but then I'm a middle class person working a high skilled job in London. I don't expect the people getting the sticky end of the wicket to just shrug and say "Ah well, at least CyclopsRock is benefitting from cheap plumbers and low costs in shops due to an infinite pool of minimum wage labour."
Furthermore, I don't really think 2 months in Spain makes you an immigrant but even if it did, the idea that if you've emigrated you must, therefore, always support all forms of immigration forevermore is obviously not a logical conclusion, and it doesn't make one a hypocrite. It's also not necessarily a case of pulling the ladder up after yourself, unless you view all immigration as a single, amorphous blob. Which only idiots do.