South Korean society isn't homogeneous so as with most questions like this it depends on who you ask. His historical status was broadly eclipsed by Park Chung-hee, who was in most respects far more directly responsible for making South Korea what it is today (for good or ill). People don't necessarily tend to have a particularly strong opinion on Rhee, whereas Park continues to be an extremely divisive figure. For instance, in 2008 a major Korean newspaper ran an opinion poll on 'the greatest South Korean president': while Park came top by an overwhelming margin with 56%, Rhee came second to last with a paltry 1.9%. [1]
In contrast to Park the literature on present Korean feelings about Rhee is basically absent -- at least in English -- so I can't go into great detail on that directly with much reliability. (This absence in itself is indicative to some extent.) I can recapitulate some of the relevant history, however, because it's worth noting that a lot of the negative sentiment over Rhee does not stem from his participation in the Korean War, but from his behaviour later in his presidency and, to a lesser extent, prior to the War.
Rhee became an incredibly unpopular figure because he presided over a stagnant economy while adopting increasingly heavy-handed tactics in the political arena. The final straw came when he attempted to rig the 1960 vice-presidential elections -- vice-presidential since he was the only candidate in the presidential elections. Protests over electoral fraud led to an escalating cycle of violence that ultimately forced the US to intervene to get rid of Rhee. [2]
On the other hand, prior to the War there is a general feeling -- justified to some extent -- that Rhee was essentially parachuted in from the US as a reliable anticommunist. Rhee was inveterately Westernised -- he had spent a great deal of time in the United States and even his wife was European. Contrary to later impressions Rhee did have a popular support base in South Korea -- for one because he could play on a vestigial family link to the Yi dynasty which had ruled Korea prior to the Japanese takeover -- but his background certainly did not help his legacy once anti-American sentiment began to emerge in South Korea in force during the 1970s/80s. [3]
So while the Korean War of course is a hot-topic issue to some extent there are probably more radical reasons for Syngman Rhee to be treated with some distance by modern South Koreans -- but at the same time, public controversy over him is actually rather muted compared to his successors.
In terms of Rhee's role in the Korean War -- while there are well-known anecdotes about him prolonging the war, many anti-establishment South Koreans tend to blame America for the division of Korea in the first place rather than Rhee for the War itself, understandably given that he is understood as a second-order actor in that narrative anyway (ie an American puppet). [4]
[1] Jinwung Kim (2012), A History of Korea, p. 473.
[2] The events are recounted in Han Seung-ju (1974), The Failure of Democracy in Korea, pp. 27-31.
[3] For a brief summary see Louis Hayes, Political Systems of Asia: China, Korea, Japan, pp. 111f.
[4] See for example Meredith Woo-Cumings, 'Unilateralism and its Discontents', in David Steinberg (ed.) (2005), Korean Attitudes Toward the United States: Changing Dynamics, here p. 56.