Had you asked this question perhaps only 10 years ago the only response you may have got would be ‘yes’. If you asked the same question today, an increasing number of people would answer ‘it depends what you replace it with’, but I would answer ‘most likely not’. To understand these points of view we need to begin with a little history (don’t worry I won’t bore you with Ancel Keys)
The Lipid Hypothesis and the Diet Heart Hypothesis
The lipid hypothesis was based on the results of the Framingham study, that serum cholesterol levels were associated with the incidence of coronary heart disease (CHD). As a result, the hypothesis was that “measures used to lower the plasma lipids in patients with hyperlipidemia will lead to reductions in new events of coronary heart disease” 
When the lipid hypothesis was originally developed they couldn’t differentiate between the cholesterol contained in different lipoproteins (e.g. HDL-C and LDL-C), so all mentions to cholesterol in the blood referred to total cholesterol (total-C). Metabolic studies conducted at this time found that SFA increased total-C, PUFA decreased total-C and MUFA had no noticeable effect , which is consistent with current research . Whether dietary cholesterol increased total-C was still debatable, though many suspected it did, a view that was supported by later research in the 60’s and 70’s .
The lipid hypothesis combined with these metabolic studies led to the diet heart hypothesis, which is that by reducing total-C, reducing SFA or replacing SFA with PUFA would be expected to reduce the incidence of CHD. The diet heart hypothesis was tested in a number of clinical trials, most of which were conducted during the 60’s and 70’s, that sought to aggressively lower total-C through a substantial reductions in SFA and dietary cholesterol and doubling or trebling PUFA intake. Very few trials used a low/reduced fat diet and when it was used or recommended (e.g. by the AHA or dietary guidelines) reducing one’s fat intake was simply seen a means to lower SFA intake , which increased total-C by about twice as much as PUFA decreased it 
Low Fat for Coronary Heart Disease
Low fat diets became popular for weight loss and prevention of CHD around the 80’s and 90’s. However, the incidence of obesity increased in many industrialised countries during this period, due to an increase in energy intake (without a parallel increase in energy expenditure). In the US this was due to an increase in carbohydrates. As a result, the percentage of calories from fat declined, but absolute fat intake stayed the same . The relationship between low fat diet advice and the obesity epidemic would later lead to some fairly widespread scepticism about low fat diets, which may have been part of the reason why several health organisations later retracted their advice to eat a low fat diet.
Low fat diets declined in popularity in the 2000’s. In the later 20th century people were able to differentiate between HDL-C and LDL-C, etc. HDL-C was found to be inversely associated with CHD and the total-C:HDL-C ratio emerged as a far more predictive risk factor than total-C, taking into account that inverse association . Replacing SFA with carbohydrates was found to not improve the total-C:HDL-C ratio . In addition, there were concerns that increasing carbohydrates would elevate triglycerides and decrease LDL particle size  , altogether making carbohydrates an unattractive replacement for SFA. In support of their effects on the total-C:HDL-C ratio, meta-analyses of observational studies were not finding that total fat was associated with CHD   and/or that carbohydrate or replacing SFA with carbohydrate was inversely associated with CHD  
At about the same time, interest in low carbohydrate diets was reignited and a number of clinical trials compared a low fat diet to a low carb diet. In these trials the low carb diet was equal to or better than the low fat diet regarding weight loss and blood lipids . The improvement in blood lipids is what you would expect from replacing carbohydrate with fat . Meanwhile the low fat diet Women’s Health Initiative (which decreased fat intake by 9% of total calories, while increasing fruit and vegetable consumption) pretty much accomplished nothing besides affirming the null hypothesis 
The Return to Fat Modification
As a result, many health organisations currently say that they no longer recommend a low fat diet (which depends on how you define low fat ) and recommend replacing SFA with unsaturated fats, rather than carbohydrates. This is largely because replacing SFA with either MUFA or PUFA would be expected to lower LDL-C (which some people still use) and the total-C:HDL-C ratio (as opposed to the days of total-C where MUFA was ignored because it had no noticeable effect) . Some will distinguish between MUFA and PUFA, as meta-analyses of observational studies have not shown replacing SFA with MUFA to reduce the risk of CHD  and also there haven’t been many clinical trials on CHD where SFA is replaced with MUFA.
Instead, these people recommend replacing SFA with PUFA, particularly linoleic acid (18:2 n-6). In additional to how SFA and PUFA affect blood lipids, they may also cite evidence from observational studies and randomised controlled trials to support their position, often selecting the meta-analyses that support their position most strongly (e.g. citing    instead of    or the Cochrane meta-analysis )
Indeed, while advice to replace SFA with PUFA is very mainstream, there are some researchers who disagree with it. This alternative position is often be argued from a different interpretation of the evidence  and proposed mechanisms suggesting that increasing omega 6 (or the omega 6 to omega 3 ratio) may be harmful 
With these conflicting views I decided to look at the clinical trials that replaced SFA with PUFA  and the major meta-analyses . I found that sometimes the meta-analyses were inconsistent (the trials they included and which figures they used) and sometimes they made errors (some minor, some major)   . In addition, while looking at the trials it became clear very quickly that they generally weren’t well controlled interventions, almost always in favour of the experimental group (high PUFA group):
· The experimental group were also advised to reduce their intake of TFA and/or foods rich in TFA such as baked goods 
· In some trials the experimental diet was highly multifactorial, such as also increasing intake of fish and whole plant foods  
· Or there were other differences such as a lower and insufficient intake of vitamin E in the control group  or an increase in the use of cardiotoxic medications in the control group .
Therefore, I categorised trials as being ‘adequately controlled’ or ‘inadequately controlled’ and used software from the Cochrane Collaboration  to conduct my own informal meta-analysis, paying special attention to the pooled results of the ‘adequately controlled’ trials , as these most closely reflect a true test of replacing SFA with PUFA. What I found was that there was no benefit (or hint of benefit) for replacing SFA with PUFA, the risk ratio for CHD events, CHD mortality and total mortality was essentially 1.0 . This result was after excluding a very unfavourable trial that has been criticised for experimental group potentially having a higher intake of TFA (when stating their position these critics ignore that in the vast majority of the trials it’s the control group that has a higher intake of TFA, as well as all the other differences).
Therefore, my interpretation of the evidence is that:
· Replacing SFA with carbohydrate, MUFA or PUFA is unlikely to reduce CHD and mortality
· It’s unlikely that SFA is bad/toxic, or else the evidence suggests carbohydrate, MUFA and now PUFA would be equally as bad/toxic