The "laws of thought" refers to the three traditional principles said to underlie logical reasoning: identity, non-contradiction, and excluded middle. Are these principles still generally accepted? Is there serious and recent criticism of their value?
In answer to your first question, "Are these principles still generally accepted?", the empirical evidence suggests that opinion is divided.
The same evidence suggests that the answer to your second question, "Is there serious and recent criticism of their value?" is yes.
In a relatively recent survey of philosophers, only about half said they accept or lean toward classical logic (see: https://philpapers.org/surveys/results.pl). The rest either said they accept or lean toward non-classical logic, which include logics that violate those "laws of thought" you mentioned, or responded "Other".
Non-classical logics generally reject (or give new meaning to) at least one of these traditional "laws of thought." Examples:
- Many-valued logic, which goes back to Aristotle, and which doesn't accept the traditional law of excluded middle
- Intuitionist logic, which also doesn't include the law of the excluded middle (and also gets rid of double negation elimination)
- Non-reflexive / "Schrödinger" logic, which leaves out or loosens the law of identity (see Schrödinger, E., 1952, Science and Humanism).
- Linear logic, where the law of excluded middle gets very weird interpretations (https://plato.stanford.edu/entries/logic-linear/)
One last note: Dialetheism is a view that gets some attention. It's not a formal system of logic like the ones mentioned above. Dialetheism, in its crazier form, is the thesis that there can be a true statement whose negation is also true. In a saner (but still crazy) form, it is the thesis that sometimes the best theory is contradictory. Outside of Western philosophy, I would guess that Dialetheism is actually quite popular (Zen Buddhists, for example, often seem to accept it), but I don't have empirical evidence to support that conclusion.