Good question(s)! I'll be focusing on pro-Republican volunteers who served in the International Brigades, not least because in a specifically British context, there were so few pro-Franco volunteers that it's hard to speak meaningfully about their postwar experiences (Ireland is another matter, of course).

The easiest part of the question to answer is regarding their communities - those that survived Spain were welcomed home as heroes for the most part. This was a self-fulfilling prophecy though, as they had generally volunteered precisely because they lived in communities (in both a local and political sense) which responded in particular ways to the conflict. After the remaining volunteers were withdrawn in late 1938, large crowds gathered to meet their trains in places that had seen large contingents depart like London and Glasgow, and similar welcomes were repeated on a smaller scale elsewhere. Over the winter of 1938-9, there were frequent memorial meetings, rallies and fundraising events. These events were popular among people who supported the Republic, and largely ignored by those who were more neutral (or a smaller minority who actively supported Franco).

There were always a trickle of returning volunteers throughout the conflict before this point (repatriation was sometimes possible due to health or family reasons, and some succeeded in deserting and fleeing Spain), and for these individuals the reception they received depended mostly on their local standing: were they popular in their community, had they received media coverage, had they been sold as heroes by pro-Republican groups, especially the Communist Party of Great Britain (CPGB), who had organised the British contingent in the International Brigades and whose newspaper (the Daily Worker) had covered their exploits extensively. Depending on these factors, some veterans were highly celebrated and others mostly ignored. In rarer cases, volunteers who had gotten home (by deserting and otherwise) and then spoken out against the Republic or the International Brigades got a much more frosty reception, to the extent that at least one former volunteer who'd gone to the Daily Mail (then as now highly unsympathetic to left-wing causes) after returning home was beaten up on the street in his hometown of Dundee. More commonly though, disgruntled former volunteers were safe enough from physical harm, though CPGB and other pro-Republican groups would keep an eye on them and do their best to discredit them if they went public with their grievances.

The question of government treatment is much less straightforward. There's no doubt that the Security Service (MI5) and local police considered former volunteers to be persons of interest - they had monitored British volunteers leaving for Spain from the outset, and more broadly had long been institutionally focused on combating left-wing revolutionary threats. Some were undoubtedly subject to ongoing surveillance (we know because their files have been released and can be browsed at the UK's National Archives). But there is a more difficult underlying question as to how widespread this kind of treatment actually was (only a small minority of former volunteers have such files), and crucially whether being a Spanish veteran was in itself a cause for such treatment.

Perhaps the largest area of controversy here is less whether there was passive surveillance on some scale, but rather whether the veterans were actively discriminated against. Given the timing of their return, the main area of contention here is whether the volunteers faced discrimination when it came to trying to participate in the Second World War. While some had quite prominent and successful careers in the armed forces, the more prominent popular narrative has long been of exclusion, victimisation and waste. Despite the volunteers’ experience in modern warfare, despite their demonstrable commitment to opposing fascism, they were shunned by the British state and prevented from contributing to the war effort. They, in the parlance of the American volunteers, became ‘Premature Anti-fascists’, a label of ironic pride in the face of official absurdity.

Historians of British involvement in the Spanish Civil War have long been aware that the ex-volunteers faced highly variable treatment at the hands of the state during the Second World War, but have struggled to rationalise or explain exactly what was going on. Clearly, the boundaries to participation were not concrete, otherwise many ex-volunteers’ distinguished wartime service would have been impossible. Equally, there are many known cases where individuals faced obvious or implied discrimination, so there clearly were some official efforts to manage or restrict their involvement in the war effort. This problem is compounded by the absence of wartime records or testimony from the bulk of ex-volunteers – making building a representative picture very challenging. While we have a very complete set of records relating to their time in Spain, it's much harder to build a general, representative picture of their postwar trajectories. While there's some evidence that army recruiters saw the Spanish veterans as a dangerous category that should be excluded, this evidence comes only from before the war itself - in other words, we can't be sure the the demands of actually fighting a war (in which manpower became very scarce) didn't lead to a change in policy.

Cont. below.